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Generalized hesitant fuzzy sets and their application in decision support system
Abstract
Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several possible memberships for an element to a set. During the evaluating process in practice, however, these possible memberships may be not only crisp values in [0, 1], but also interval values. In this study, we extend hesitant fuzzy sets by intuitionistic fuzzy sets and refer to them as generalized hesitant fuzzy sets. Zadeh’s fuzzy sets, intuitionistic fuzzy sets and hesitant fuzzy sets are special cases of the new fuzzy sets. We redefine some basic operations of generalized hesitant fuzzy sets, which are consistent with those of hesitant fuzzy sets. Some arithmetic operations and relationships among them are discussed as well. We further introduce the comparison law to distinguish two generalized hesitant fuzzy sets according to score function and consistency function. Besides, the proposed extension principle enables decision makers to employ aggregation operators of intuitionistic fuzzy sets to aggregate a set of generalized hesitant fuzzy sets for decision making. The rationality of applying the proposed techniques is clarified by a practical example. At last, the proposed techniques are devoted to a decision support system.
... At present, the research on fuzzy sets is mostly around IFS and HFS. In terms of theoretical innovation, Chen [7] proposed interval valued hesitation fuzzy sets in combination with IVFS and HFS, Qian [8] proposed generalized hesitant fuzzy sets(GHFS) based on IFS and HFS. Palanikumar [9] present the idea of a possibility Pythagorean cubic fuzzy soft set and discuss how it may be used to solve practical issues. ...
... Definition 7: Let X be a non-empty set, a generalized hesitant fuzzy set M can be defined as [8]: ...
... Given two GHFEs Gh 1 and Gh 2 , for λ > 0, we have [8]: ...
Traditional intuitionistic fuzzy sets and hesitant fuzzy sets will lose some information while representing vague information, to avoid this problem, this paper constructs weighted generalized hesitant fuzzy sets by remaining multiple intuitionistic fuzzy values and giving them corresponding weights. For weighted generalized hesitant fuzzy elements in weighted generalized hesitant fuzzy sets, the paper defines some basic operations and proves their operation properties. On this basis, the paper gives the comparison rules of weighted generalized hesitant fuzzy elements and presents two kinds of aggregation operators. As for weighted generalized hesitant fuzzy preference relation, this paper proposes its definition and computing method of its corresponding consistency index. Furthermore, the paper designs an ensemble learning algorithm based on weighted generalized hesitant fuzzy sets, carries out experiments on 6 datasets in UCI database and compares with various classification algorithms. The experiments show that the ensemble learning algorithm based on weighted generalized hesitant fuzzy sets has better performance in all indicators.
... At times, it is tedious to determine the membership degree of an element into the fixed set. IFS provide the solution using the hesitation index which is characterized by the membership and non-membership function [9]. ...
... From the literature review, many studies have discussed the protection of privacy breaches [2,3] and balancing the data utility to some extent. Cryptographic approach [13,14], l-diversity and k-anonymity [9,17] are mostly used for data perturbation. These approaches are efficient in securing data privacy but result in higher computation costs and temporal attacks [17] due to dynamic data pooling in the repositories. ...
... The quasi-identifiers from the adult income, bank marketing and lung cancer dataset is applied on the Eqs. (4,5,6,9,10,12,13) to get the membership value ...
Data sharing to the multiple organizations are essential for analysis in many situations. The shared data contains the individual’s private and sensitive information and results in privacy breach. To overcome the privacy challenges, privacy preserving data mining (PPDM) has progressed as a solution. This work addresses the problem of PPDM by proposing statistical transformation with intuitionistic fuzzy (STIF) algorithm for data perturbation. The STIF algorithm contains statistical methods weight of evidence, information value and intuitionistic fuzzy Gaussian membership function. The STIF algorithm is applied on three benchmark datasets adult income, bank marketing and lung cancer. The classifier models decision tree, random forest, extreme gradient boost and support vector machines are used for accuracy and performance analysis. The results show that the STIF algorithm achieves 99% of accuracy for adult income dataset and 100% accuracy for both bank marketing and lung cancer datasets. Further, the results highlights that the STIF algorithm outperforms in data perturbation capacity and privacy preserving capacity than the state-of-art algorithms without any information loss on both numerical and categorical data.
... Fuzzy sets are often employed when dealing with real-world inaccuracies. While the traditional fuzzy set conveys only membership and non-membership information, Atanassov's intuitive complex numbers provide extra information for scenario description [9]. IFS is effective in dealing with intrinsically erroneous or unreliable judgments, which may hinder DMs to convey their confirmation, rejection, and reluctance of decision-making activities [10], [11]. ...
... where is the weight for the method with the greatest group utility, and is the weight of the individual's regret. ̃ Extremely essential/preferred (5,7,9) 9 ...
... ̃ Extremely more (7,9,9) DOI ...
The Malaysian government’s support for offshore wind power production has led to an increase in a few proposals. An important factor in the overall efficiency of any offshore wind farm is the site selection process, which is a multi-criteria decision-making (MCDM) task. However, classical MCDM techniques often fail to choose a suitable site because of three main challenges. First, compensation is regarded as a problem in the processing of information. Second, data usage and data leakage are often ignored in the decision-making process. Third, interaction difficulty in fuzzy environments is easily ignored. This study provides a framework for making site selection decisions for offshore wind farms while addressing the constraints. Fuzzy VIKOR is used in the second stage of the AHP process to analyze the site’s results with respect to evaluation criteria for offshore wind farms. A comprehensive index system, which incorporates the veto criteria and evaluation criteria for selecting offshore wind power station sites, is devised. Then, the system is used to transmit imprecise information to decision makers by using a triangular fuzzy set. Likelihood-based valued comparisons indicate that imprecise choice information can be correctly used, and issues of information loss can be logically avoided. A case study of Malaysia is used to demonstrate the validity and practicality of the site selection technique. This research offers a theoretical basis for accurate offshore wind power evaluation in Malaysia.
... As the demand consciousness that is stored in a customer's mind is implicit and tacit in nature, extracting this parameter with numerical values is difficult. Zadeh [30] argued that the theory of fuzzy information granulation was central in human reasoning processes. Thus, fuzzy theory and decision-making approaches that include group and multi-criteria technologies present an extraordinary contribution to QFD [8,11,16]. ...
... Second, from an academic perspective, the technologies of fuzzy mathematics are employed to address uncertain information fusion in multi-enterprise manufacturing contexts. Fuzzy logic, which provides the machinery for fuzzy information granulation, has long played a major role in the applications of expressing and addressing uncertainty [30]. The outranking relation of fuzzy multicriteria group decision-making methodology is systematically designed to allow the rendering of decisions about multi-enterprise collaborative schemes. ...
This paper presents an operational framework of unstructured decision-making approach involving quality function deployment (QFD) in an uncertain linguistic context. Firstly, QFD is extended to the multi-enterprise paradigm in a real-world manufacturing environment. Secondly, hesitant fuzzy linguistic term sets (HFLTSs), which facilitate the management and handling of information equivocality, are designed to construct a house of quality (HoQ) in the product planning process. The technique of computing with words is applied to bridge the gap between mechanisms of the human brain and machine processes with fuzzy linguistic term sets. Thirdly, a multi-enterprise QFD pattern is formulated as an unstructured decision-making problem for alternative infrastructure project selection in a manufacturing organization. The inter-relationships of cooperative partners are directly matched with a back propagation neural network (BPNN) to construct the multi-enterprise manufacturing network. The resilience of the manufacturing organization is considered by formulating an outranking method on the basis of HFLTSs to decide on infrastructure project alternatives. Finally, a real-world example, namely, the prototype manufacturing of an automatic transmission for a vehicle, is provided to illustrate the effectiveness of the proposed decision-making approach.
... For customized product manufacturer selection, imprecise and vague information are inherent since the ambiguity of decision-makers' perceptions and the complexity of decision-making issues. Numerous valuable fuzzy approaches have been developed and extended to deal with the uncertainty information in multi-criteria decision-making (MCDM) problems, such as fuzzy sets [45], vague sets [49], rough sets [10,11], hesitant fuzzy sets [32], grey theory [9], and basic uncertain information [15]. Recently, Yager [43] introduced the concept of q-rung orthopair fuzzy sets (q-ROFSs) to express the uncertain and imprecise information that arises in real circumstances [50]. ...
... Then, based on Eqs. (31)- (32), the decision model is established below: ...
Selecting the appropriate manufacturer is important in customized product development because a poor selection may delay the delivery schedule, increase costs, and even affect product quality. This selection task inherently involves ambiguous and imprecise information from decision-makers. The q-rung orthopair fuzzy (q-ROF) sets theory has been proven as a valuable instrument to model human uncertain expressions. However, the existing q-ROF score functions, an essential tool to rank q-ROF values, have some deficiencies, such as generating counterintuitive solutions and antilogarithm or division by zero problems. Furthermore, little research presented the modified best-worst methods (BWM) under q-ROF environments. Nevertheless, these models only generate crisp weights rather than q-ROF weights, which is against the original intention of the q-ROF BWM. To address these problems, this paper first introduces a novel q-ROF score function for measuring q-ROF values. A new q-ROF-BWM is then presented based on the q-ROF preference relations to determine the fuzzy criteria weights. Subsequently, an improved weighted aggregated sum product assessment (WASPAS) with q-ROF settings is presented. Based on them, an integrated q-ROF-BWM-WASPAS model is introduced to rank manufacturers. Additionally, a case study, sensitivity analysis, and several comparisons are conducted to illustrate and validate the usefulness of the developed model.
... Complex hesitancy fuzzy graph has be discussed by AbuHijleh [1]. Qian [7]and Talafha et al [11] worked on complex hesitancy fuzzy sets and decision making. Veeramani and Suresh [17]developed the operations on complex fuzzy graph. ...
In this paper, Complex Hesitancy Fuzzy Graph (CHFG) is analyzed and we have discussed new concepts in CHFG such as Complete CHFG with example. Further we defined some operations on Complex Hesitancy Fuzzy Graph such as direct product, semi strong product and strong product. Also fundamental theorems and their apllications will be examined. Additionally, new ideas in the density of a CHFG and balanced complex Hesitancy fuzzy graph have been introduced in this work.
... Torra [29] extended the FS concept to include the hesitant fuzzy set (HFS) concept. The difficulty in building the MD can be handled in circumstances where it arises from hesitancy among a few select values rather than from a margin of error or a specific probability distribution of the likely values [30] . In contrast to the FS and its other generalizations, the HFS can thus more accurately represent people's reluctance to express their preferences over items. ...
... Nonetheless, certain limitations in HFS, such as information loss and the oversight of occurrence probabilities, were identified [14]. Addressing these issues, Qian et al. [18] introduced PHFSs, integrating probability elements into HFS. Constructed on this basis, Batool et al. [19] improved the idea even more by introducing Pythagorean PHFSs, which are limited by the requirement that the square sum of the positive and negative hesitant adhesions' degrees be less than or equal to 1. ...
... In fuzzy sets theory, distance and similarity measures are important topics to study. In numerous scientific disciplines, including decision-making [11,26], machine learning, clustering analysis, pattern recognition, medical diagnosis [37] and market prediction [17], various authors have made significant use of it. As a new extension of Fuzzy sets, HBFSs have a large scope to develop new operations and measures (Information, Knowledge, Entropy, Distance and Similarity). ...
... As a result, in this framework, it is difficult to model the hesitation of the DMs on the "right" value to attribute. Since this hesitation can make an appearance while modeling the uncertainty, HFS has seen a boom in its applicability in recent years, both in terms of qualitative (Rodriguez et al. 2011) and quantitative (Qian et al. 2013;Chen et al. 2013;Yu 2013;Zhu et al. 2012) contributions. Nevertheless, the financial applications of HFS are still limited. ...
Decision support systems are a mixture of different methods and tools combined by machine learning approach. This study uses the most important machine learning techniques (logistic regression, artificial neural networks, and support vector machines) and the expert-based method (fuzzy analytic hierarchy process and hesitant fuzzy numbers) to study some financial markets dynamics. The objective of the study is to examine the main approaches developed by theory and operational practice for the purposes of conceptual representation, management and quality assessment. Different tools are applied to support decisions makers, such as AHPSort II to model the hierarchical structure, FAHP to determine weights in the construction of the matrix of the pairwise comparison and hesitant fuzzy sets (HFS) to better represent the preferences of the decisions makers.
... After that, Torra [2] proposed the hesitant fuzzy sets (HFSs), which further enriched the theory and application of fuzzy sets. Besides, many scholars have made research on HFSs, which have been extended into hesitant fuzzy linguistic term sets [3], interval value-hesitant fuzzy sets [4], dual-hesitant fuzzy sets [5], generalized hesitant fuzzy sets [6], and hesitant triangular fuzzy sets [7] and so on in recent years. ...
Probability hesitation fuzzy sets(PHFSs) have been paid increasing attention in the fuzzy domain nowadays, and correlation coefficient is becoming an important research content in fuzzy data analysis, many scholars have been conducted relevant researches on it. However, the existing correlation coefficients between PHFSs have some limitations, such as not considering the number of membership degrees and having counter-intuitive phenomenon to some extent. Therefore, we propose the mixed correlation coefficient between PHFSs. To begin with, we give the concepts of the average, variance, and length ratio of PHFE to illustrate the integrity, distribution, and length. Then, we define the average, variance, and length three correlation coefficients respectively on the above basic concepts. Furthermore, we construct the mixed correlation coefficient through combining these basic correlation coefficients, and extend to weighted form in addition, which addresses the issues of the available correlation coefficients. Finally, we utilize proposed correlation coefficient to analysis problems of data association and decision making. The effectiveness and rationality of the proposed method is illustrated at length.
... Xia and Xu [49] established the following comparison procedure for two HFEs: Definition 2: [50] For an HFE G, the score function is defined as: ...
Intuitionistic hesitant fuzzy sets, which enable the representation of an element’s membership and non-membership as a set of multiple possible values, offer significant utility in describing uncertainty in various aspects of people’s daily lives. Fundamental mathematical techniques known as intuitionistic hesitant fuzzy aggregation operators are employed to merge multiple inputs into a single result based on predetermined criteria. However, conventional approaches that rely on classic intuitionistic hesitant fuzzy aggregation operators have faced criticism due to their limited understanding of criteria characterization. We introduce two novel operators, namely the intuitionistic hesitant fuzzy partitioned Maclaurin symmetric mean (IHFPMSM) and intuitionistic hesitant fuzzy weighted partitioned Maclaurin symmetric mean (IHFWPMSM), which draw inspiration from the partitioned Maclaurin symmetric mean concept. Subsequently, we thoroughly examine various characteristics and special cases of these operators. Building upon the IHFWPMSM operator, we propose a novel multiple-criteria decision-making (MCDM) method that effectively selects the most suitable alternative from a set of options. To demonstrate the effectiveness of our proposed approach, we discuss a systematic methodology for selecting the optimal location for shoe company construction. Lastly, we demonstrate the superior prevalence and effectiveness of the developed approach through comprehensive comparative and sensitivity analyses, surpassing the capabilities of existing approaches.
... However, in practice, DMs from various disciplines and with different degrees of expertise employ linguistic terminology to convey their assessments and preferences while resolving qualitative collaborative decision-making issues. The majority of facts and information contained in expert judgements are subjective and intrinsically non-numeric, which leads to ambiguity, imprecision, fuzzy theory, such as interval-valued fuzzy sets (Vahdani & Hadipour, 2011), intuitionistic fuzzy sets (Wu & Chen, 2011), Pythagorean fuzzy sets (Akram et al., 2020;Habib et al., 2022;Luqman et al., 2021), hesitant fuzzy sets (Akram, Luqman et al., 2023;Qian et al., 2013), and so on, to handle ambiguity and undecidedness in human opinions. For navigating with imprecision, fuzzy sets are a very effective and frequently employed technique. ...
Rough set theory is an efficient and flexible tool for the removal of unnecessary or irrelevant attributes present in the evaluation process and interval rough numbers (IRNs) are designed to effectively treat the inherited uncertainty in human assessments in the multi-criteria decision making (MCDM) problems. In the ELECTRE (ELimination and Choice Expressing REality) family of MCDM techniques, the options that are outranked by others are eliminated in order to present the most accurate and feasible set of actions or solutions to the core problem. In order to deal with the subjectivity and unpredictability in judgements made by experts without much prior knowledge, membership functions, or other changes, this research study offers an innovative MCDM methodology that integrates interval rough numbers, Step-wise Weight Assessment Ratio Analysis (SWARA), and the ELECTRE I method (named as IRN SWARA ELECTRE I Model). To examine the uncertainty in linguistic terms, IRNs are employed, but intervals rather than single fixed values are used. Three kinds of interval rough concordance and discordance sets are defined to build the proposed strategy. The criteria weights are computed by employing effective and simplified technique of interval rough SWARA having the ability to deal with preference ratings in the form of IRNs. The applicability of the proposed methodology is demonstrated by solving a case study related to assessment of machine tool remanufacturing models. To elaborate the authenticity, rationality, out-performance, and efficacy of findings, a comprehensive comparative study as well as sensitivity analysis are conducted.
... FCE was proposed by Wang Peizhuang, a Chinese scholar. It is a comprehensive evaluation method based on the membership theory of fuzzy mathematics, which can describe complex systems in line with reality and is widely used in automatic control, economic management, bioengineering, environmental science, psychology, philosophy and many other fields [45][46][47]. ...
The coal mine in deep mining can easily form a compound dynamic disaster with the characteristics of rock burst and gas outburst. In this paper, the analytic hierarchy process (AHP) and the entropy weight method (EWM) are combined, and the fuzzy comprehensive evaluation (FCE) secondary evaluation model of compound dynamic disaster is proposed to evaluate the risk of compound dynamic disaster, which avoids the problems of the imperfect evaluation index system and strong subjectivity of index weight. Based on the statistical analysis of typical compound dynamic disaster cases in China, three first-level indicators were established, and sixteen second-level indicators were developed. The verification results show that the accuracy and weight are better than the traditional evaluation methods. Combined with geological and mining data, the compound dynamic disaster risk assessment was carried out on the second mining area of mine B, in the Pingdingshan mining area, and the result was grade II (weak risk). Corresponding prevention measures and parameters were implemented, and no compound dynamic disaster occurred during the working face excavation.
... As a result, in this framework, it is difficult to model the hesitation of the DMs on the "right" value to attribute. Since this hesitation can make an appearance while modeling the uncertainty, HFS has seen a boom in its applicability in recent years, both in terms of qualitative [69] and quantitative [70][71][72][73] contributions. Nevertheless, the financial applications of HFS are still limited. ...
Decisions Support Systems are a mixture of different methods and tools combined by machine learning approach. This study uses the most important machine learning techniques (logistic regression, artificial neural networks, and support vector machines) and the expert-based method (fuzzy analytic hierarchy process and hesitant fuzzy numbers) to study some financial markets dynamics. The objective of the study is to examine the main approaches developed by theory and operational practice for the purposes of conceptual representation, management and quality assessment. Different tools are applied to support decisions makers, such as AHPSort II to model the hierarchical structure, FAHP to determine weights in the construction of the matrix of the pairwise comparison and Hesitant Fuzzy Sets (HFS) to better represent the preferences of the decisions makers.
... Moreover, Pythagorean hesitant fuzzy sets (PHFSs) were surveyed by Khan [14]. Also, papers based on generalization of hesitant fuzzy sets can be ordered as follow; Dual interval-valued hesitant fuzzy sets (DIVHFS) [15], Interval-valued hesitant fuzzy sets (IVHFS) [16], Generalized hesitant fuzzy sets (GHFS) [17], Triangular hesitant fuzzy sets (THFS) [18], Multi hesitant fuzzy sets [19]. ...
This paper aims to present some novel ordering methods to obtained Bipolar valued probabilistic hesitant fuzzy sets (BVPHFS) by extending probabilistic hesitant fuzzy sets (PHFS). PHFS is a strong version of hesitant fuzzy sets (HFS) in terms of evaluated as probabilistic of each element in HFS. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Then, some properties of BVPHFS are surveyed. Further, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed by proposing an example and results are compared in their own.
... However, HFS eventually revealed the massive loss of information, and the occurrence probability of each element was disregarded [69]. The study conducted by [73] overcame these limitations by adding the probability into the HFS and proposed the probabilistic hesitant FS. Later, [74] improved the probabilistic hesitant FS and proposed the notation of Pythagorean probabilistic hesitant FSs. ...
The benchmarking of agri-food 4.0 supply chain (Agri4SC) falls under the multiple criteria problem in supply chain visibility (SCV) and supply chain resource integration (SCRI) for improving data analytics capabilities and achieving sustainable performance (SP). It is considered a multiple criteria decision-making (MCDM) problem due to three main concerns, namely, multiple Agri4SC evaluation criteria including the SCV, SCRI and SP criteria. These criteria have relative importance and trade-offs. Despite the tremendous efforts over the last years, none of the developed Agri4SCs have met all of the essential Agri4SC evaluation criteria. Another concern raised in the evaluation and benchmarking of the Agri4SC is the uncertainty of experts. Thus, the main contribution of this research is to propose an Agri4SC benchmarking framework in SCV and SCRI for improving data analytics capabilities and achieving SP based on an extension of the proposed Fermatean probabilistic hesitant fuzzy sets (FPHFSs) and MCDM methods. The methodology process is divided into six main parts. Firstly, an Agri4SC decision matrix is formulated based on the intersection of the Agri4SC alternatives and criteria to cover multiple Agri4SC evaluation criteria issues. Secondly, novel FPHFSs are proposed along with their operational laws, score function, accuracy function, Fermatean probabilistic hesitant fuzzy average mean operator and Fermatean probabilistic hesitant fuzzy weighted average operator. The FPHFS can encompass more sophisticated and uncertain evaluation information. Thirdly, Fermatean probabilistic hesitant fuzzy weighted zero inconsistency is formulated to assign weights to the evaluation criteria. Fourthly, the Fermatean probabilistic hesitant fuzzy decision by opinion score method (FPH-FDOSM) is formulated and used to score the alternatives that were evaluated subjectively based on SCV criteria. Fifthly, the FPH-FDOSM-based multi attributive ideal-real comparative analysis (MAIRCA) scoring method with equal probabilities is proposed to score Agri4SC alternatives that were evaluated subjectively based on weighted economic, environmental and social factors. Lastly, the MAIRCA ranking method with unequal probabilities is introduced to benchmark Agri4SC alternatives that were evaluated objectively based on the weighted subcriteria of SP and the trade-offs amongst the identified criteria. The robustness and reliability of the results are tested via sensitivity analysis and Spearman’s correlation coefficient.
... In (Riera, Massanet, Herrera-Viedma, & Torrens, 2015), a fuzzy decision-making model based on discrete fuzzy numbers is proposed for solving MCDM problems. In (Qian, Wang, & Feng, 2013), HFS is transformed into intuitionistic fuzzy sets and subsequently used to develop a decision support system for MCDM problems. Hesitant fuzzy linguistic Entropy and cross-entropy integrated with the queuing method is used to solve MCDM in (Gou, Xu, & Liao, 2017). ...
This paper introduces a new methodology for solving Multi-Attribute Decision Making (MADM) problems under hesitant fuzzy environment. The uncertainty in Hesitant Fuzzy Elements (HFE) are derived by means of entropy. The resulting uncertainty is subsequently used in HFE to derive a single representative value (RV) of alternatives in each attribute. Our work transforms the RVs into their linguistic counterparts and then formulates a methodology for pairwise comparison of the alternatives via their linguistically defines RVs. The Eigen vector corresponding to maximum Eigen value of the pairwise comparison matrix prioritize the alternatives in each attribute. The priority vectors of the alternatives are aggregated to derive the weights of the attributes using Quadratic programming. The weighted aggregation of the attribute values provides the ranking of the alternatives in MADM. An algorithm is written to validate the procedure developed. The proposed methodology is compared with similar existing methods and the advantages of our method are presented. The robustness of our methodology is demonstrated through sensitivity analysis. To highlight the procedure a car purchasing problem is illustrated.
... As a result, as compared to the FS and its other generalizations, the HFS can more exactly reflect people's reluctance to express their preferences for items. IFS and HFS were then integrated to create a new HFS known as the intuitionistic hesitant fuzzy set (IHFS) [19]. The main idea is to create a case in which, instead of an individual MD and a non-membership degree (ND), humans hesitate between a group of MD and ND and need to represent such a reluctance. ...
The Fermatean fuzzy set concept, which was developed by merging Fermatean fuzzy sets with hesitant fuzzy sets, may be utilized in practice to ease the solution of complex multi-criteria decision-making (MCDM) issues. The idea of a Fermatean hesitant fuzzy set is introduced first, followed by the operations associated with this concept. Aggregation operations based on Fermatean hesitant fuzzy sets are provided, and their fundamental features are investigated. A novel MCDM approach obtained using operators has been developed to choose the best choice in practice. Finally, the efficiency of the recommended strategies was demonstrated using a lung cancer case study.
... In comparison to the SFQN1 approach, the numerical results of SFQM1 methods are better in terms of absolute error and CPU time, as shown in Tables 1(a,b)-4(a,b) and Figures 1-6. Using the same methodologies as described in this article, and using technique of weight function we can construct optimal fourth-order efficient numerical iterative methods for solving systems of fuzzy linear and nonlinear equations using more generalized fuzzy numbers, i.e. intuitionistic fuzzy number [13], trapezoidal fuzzy number [37], bipolar fuzzy number [40], hesitant fuzzy number [42][43][44], etc. ...
In this research, we suggested a numerical iterative scheme for investigating the numerical solution of fuzzy linear and nonlinear systems of equations, particularly where the linear or nonlinear system co-efficient is a crisp number and the right-hand side vector is a triangular fuzzy number. Triangular fuzzy systems of linear and nonlinear equations play a critical role in a variety of engineering, scientific challenges, mathematics, chemistry, physics, artificial intelligence, biology, medical, economics, finance, statistics, machine and deep learning, computer science, robotics and smart cars, programming, in the military and engineering industries, linear and nonlinear programming problems and traffic flow problems. In biomedical engineering, fluid flow problems, and differential equations, triangular fuzzy linear and nonlinear systems of equations also play a key role in determining the level of uncertainty. Convergence analysis illustrates that the proposed numerical technique's order of convergence for solving a triangular fuzzy system of linear and nonlinear equations is three. The newly developed numerical scheme was then applied to solve several triangular fuzzy boundary value problems. In terms of convergence rate, computing time, and residual error, numerical test problems indicate that the newly developed methods are more efficient than the current methods in the literature.
... Therefore, Torra and, Torra and Narukawa [4,5] have presented to Hesitant fuzzy sets. Then, this concept has been converted to different clusters, Dual hesitant fuzzy sets [22], Generalized hesitant fuzzy sets [23], Triangular hesitant fuzzy set [24], multi-hesitant fuzzy sets [25], then Pythagorean Hesitant Fuzzy Set [26] was defined by combining hesitant fuzzy sets and Pythagorean fuzzy sets. Moreover, Zhang and others [44] put forward Interval Valued Pythagorean Hesitant Fuzzy Set and gave its application to MCDM, Wei and Lu, [27] Tang and Wei [28] proposed Dual hesitant Pythagorean fuzzy Hamacher aggregation operators and Dual hesitant Pythagorean fuzzy information in a decision making method, Khan et al. [29] aggregated Pythagorean hesitant fuzzy information. ...
In this paper, we introduce Interval valued q- Rung Orthopair Hesitant fuzzy sets (IVq-ROHFS) with motivation of Interval valued pythagorean Hesitant fuzzy sets [44] as a new concept. Then, we give some basic operations as complement, union, intersection, addition, scalar multiplication, scalar power. Also, we combine to (IVq-ROHFS) and choquet integral , together with aggregating operators, and develop to Interval valued q- rung orthopair hesitant fuzzy Choquet averaging operator (IVq-ROHCA) and Interval valued q- rung orthopair hesitant fuzzy Choquet geometric operator (IVq-ROHCG). Then, we offer to indicate soft approach of proposed IVq-ROHCA and IVq-ROHCG an example adopted from Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS (IVIHCI) [43]. The obtained results are agreement with IVIHCI but presented IVq-ROHCA and IVq-ROHCG have more advantages than existing structures as Interval-valued intuitionistic hesitant fuzzy sets (IVIHFS), interval-valued Pythagorean Hesitant fuzzy sets (IVPHFS) with reasons changing according to need, requirement, prefer of decision makers and moreover, being IVIHFS and IVPHFS are special cases of IVq-ROHFS. It is open from comparative analysis that the while some of offered approaches are giving no solution for some values, our operators present to needed results.
... Because of this, the HFS, as opposed to the FS and its other generalizations, can more accurately reflect people's reluctance to express their preferences over objects. A new HFS called IHFS was created later by combining HFS with IFS [21]. The basic idea is to create a scenario in which people pause between a group of MD and ND rather than an individual MD and ND, and they need to represent such a reluctance. ...
The Hesitant Fuzzy Set, a generalization of fuzzy sets, is a crucial tool for resolving the challenges associated with defining an element’s membership in a set when there is uncertainty regarding several separate values in decision-making situations. To ensure that the conditions under which experts evaluate an alternative in likely membership values and non-membership values are operational in this study, a Fermatean hesitant fuzzy set is provided. To implement multi-attributed group decision-making problems, new defined sets’ aggregate operators are defined. The primary characteristics of the new sets were investigated. Two interval-valued values are compared using a new score function and an accuracy function. Finally, a numerical example exemplifies the viability, applicability, and efficacy of the suggested approach.
... Normalized hesitant fuzzy synergetic weighted distance measure was introduced by Peng et al. (2013). Qian et al. (2013) studied generalized HFSs. They also defined the score function and consistency function and operations of generalized HFSs. ...
The fuzzy set (FS) and its generalizations are important tools in modelling decision-making problems. Although the FS is a successful tool in modeling one-dimensional information, it is insufficient in modeling two-dimensional information. This weakness is corrected with complex fuzzy set (CFS), which is a successful structure in representing two-dimensional information. In addition, the hesitant fuzzy set (HFS) is a very useful argument in group decision-making problems. The complex neutrosophic set (CNS) is an extension of the FS that was recently identified and attracted the attention of researchers. In this study, the concept of hesitant complex neutrosophic set (HCNS) is defined by combining the concepts of CNS and HFS. Also, distance measures between two HCNSs based on Euclidean, Hamming and Hausdorff distance measures are introduced and some relationships between them are examined. Moreover, a decision-making method using the proposed distance measures has been developed and an example including the computer purchasing problem is given to show the application process of the developed method.
... Then, Torra [2] and Torra and Narukawa [3] developed hesitant fuzzy sets which the membership degrees of an element of universe set to a given set only by crisp numbers between 0 and 1. So far, many authors have studied on the fuzzy sets and hesitant fuzzy sets in [4][5][6][7][8][9][10][11][12][13] and especially in on real number set R. For example, Fahmi et al [14,15] have defined the concept of triangular cubic hesitant fuzzy number. Amin et al. [16] have propound aggregation operators for triangular cubic linguistic hesitant fuzzy set. ...
As an extension of the trapezoidal fuzzy number, the generalised trapezoidal hesitant fuzzy number is an effective mathematical tool for handling uncertainty and vagueness in decision-making problems. Considering that the quasi-distance measure has a strong ability to process and analyse data, we initiated some novel quasi-distance measures to measure the strength of the relationship between generalised trapezoidal hesitant fuzzy numbers in this paper. Moreover, based on the proposed measures, a new multi-criteria decision-making approach is proposed to address uncertain real-life situations. Finally, a practical application of the proposed approach is also illustrated to demonstrate the effectiveness and applicability.
... Quir'os et al. [14] investigated the entropy of finite interval-valued hesitant fuzzy set(IVHFS). Qian et al. [13] investigated the generalized hesitant fuzzy set(GHFS) and applied in decision making. Zeng et al. [42,43] combined interval-valued and linguistic term with hesitant fuzzy theory through weights and applied in group decision making. ...
A dual hesitant fuzzy set (DHFS) describes the uncertainty in the real world by using the membership degree and nonmembership degree. It can collect fuzzy information comprehensively and apply them into decision‐making tasks efficiently. In this article, we extract some characteristics, such as the average function, variance function, hesitancy degree to describe a dual hesitant fuzzy element, and develop novel distance measures of DHFSs based on these characteristics. Further, we investigate their properties and prove the triangle inequality of distance measure. Finally, we apply it in practical medical diagnosis to illustrate the validity of our proposed distance measures.
... To express such situations more effectively, the concept of hesitant fuzzy sets has been introduced in [23]. There had been further extensions in hesitant fuzzy sets also, such as the intuitionistic hesitant fuzzy sets [24], q-rung orthopair hesitant fuzzy set [25] which was developed by combining the concepts of hesitant and intuitionistic fuzzy sets and hesitant and q-rung orthopair fuzzy sets, respectively. ...
This paper deals with ensemble feature selection using the q-rung orthopair hesitant fuzzy multi-criteria decision-making (MCDM) methods including VIse Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Combinative distance-based assessment (CODAS). The novalty of this paper is to design the three MCDM algorithms based on q-rung orthopair hesitant fuzzy sets with different distance and similarity measures. The well known distance and similarity measures are to be taken such as Hausdorff measure, hybrid Hausdorff and distance measure, synergetic measure, similarity for Hausdorff measure, similarity for hybrid Hausdorff and distance measure, similarity for synergetic measure, ordered Hausdorff measure, ordered hybrid Hausdorff and distance measure, similarity for ordered Hausdorff measure and similarity for ordered hybrid Hausdorff and distance measure This is the first time in the literature, an ensemble feature selection problem is modeled as a q-rung orthopair hesitant fuzzy MCDM extended to VIKOR, TOPSIS and CODAS techniques with distance and similarity measures. By using q-ROHFS VIKOR, TOPSIS and CODAS methods, a score is assigned to each feature based on the values of the preference matrix. At last, an output rank vector is produced for all features, from which the user can select the desired number of features. To prove the efficiency and optimality of our proposed method, we compared with the basic filter-based feature selections and ensemble feature selection by using feature ranking strategy. Our method is superior and efficient than the ensemble methods based on the accuracy and F-score levels.
... Intuitionistic fuzzy set is characterized by membership, non-membership and hesitancy degrees and the sum of membership and non-membership grades for each element must be ≤1. Qian et al. [87] extended hesitant fuzzy set to generalized hesitant fuzzy set by combining intuitionistic fuzzy set and hesitant fuzzy set. Cuong and Kreinovich [88] developed picture fuzzy set which is a direct extension of intuitionistic fuzzy set by incorporating the positive, neutral and negative membership grades of an element while the sum of them is ≤1. ...
Likened to the economic calamity of World War Two, the COVID-19 pandemic has sparked fears of a deep economic crisis, killed more than six million people worldwide and had a ripple effect on all aspects of life. MCDM (multi-criteria decision making) methods have become increasingly popular in modeling COVID-19 problems owing to the multi-dimensionality of this crisis and the complexity of health and socio-economic systems. This paper is aimed to review 72 papers published in 37 leading peer-reviewed journals indexed in Web of Science that used MCDM methods in different areas of COVID-19 pandemic. In this paper, data retrieval follows the PRISMA protocol for systematic literature reviews. 35 countries have contributed to this multidisciplinary research and India is identified as the leading country in this field followed by Turkey and China. Also 36 articles, namely 50% of papers are presented in the form of international cooperation. “Applied Soft Computing” is the journal with the highest number of articles whereas “Journal of infection and public health” and “Operations Management Research” are ranked in the second place. The results indicate that AHP (including fuzzy AHP) is the most popular MCDM method applied in 37.5% of papers followed by TOPSIS and VIKOR. This review reveals that the use of MCDM methods is one of the most attractive research areas in the field of COVID-19. As a result, one of the main purposes of this work is to identify diverse applications of MCDM methods in the COVID-19 pandemic. Most studies i.e. 69% (49 papers) of the papers combined various fuzzy sets with MCDM methods to overcome the problem of uncertainty and ambiguity while analyzing information. Nevertheless, the main drawback of those papers has been the lack of theoretical justifications. In fact, fuzzy MCDM methods impose heavy computational load and there is no general consensus on the clear advantage of fuzzy methods over crisp methods in terms of the solution quality. We hope the researchers who applied fuzzy MCDM methods to COVID-19-related research understand the theoretical basis of MCDM methods and the serious challenges associated with basic operations of fuzzy numbers to avoid potential disadvantages. This paper contributes to the body of knowledge via suggesting a deep vision to critique the fuzzy MCDM methods from mathematical perspective.
... Yu (2013) developed the traditional HFS into triangular fuzzy HFS, in which the membership degree of a member to a given set is shown by several possible triangular fuzzy numbers. Qian et al. (2013) extended HFSs by intuitionistic fuzzy sets and referred to them as generalized HFSs. Farhadinia (2014) extended HFSs to their higherorder type and named them as the higher-order HFSs. ...
In this paper, we introduce a new approach to solve a fully hesitant fuzzy linear programming (FHFLP) problem with hesitant fuzzy numbers (HFNs) as parameters. Using an (α,k)-cut for the HFNs, we convert this problem into some interval linear programming (ILP) problems, and solve these problems through one of the available algorithms to solve the ILP problems. Then through statistical regression analysis, we get k fuzzy numbers as the final approximate solutions, and we have proved that they are well defined. Finally, using the hesitant fuzzy arithmetic, we obtain a hesitant fuzzy value of the objective function. An example is introduced to clarify the solution process of this method, and a comparison between the optimal solutions through the proposed method to an FHFLP problem and its converted form to a fully fuzzy linear programming problem has been done. The outcomes indicate that the obtained solutions for decision variables and objective function are reasonable.
... For example, Khan et al. [22][23][24] introduced several novel similarity measures for the q-rung orthopair fuzzy sets. Zeng et al. [25,26] introduced weighted interval-valued hesitant fuzzy set and weighted hesitant fuzzy linguistic term set, and applied in group decision making, respectively, Zhu et al. [27] introduced dual hesitant fuzzy set, Chen et al. [28] and Wei et al. [29] developed interval-valued hesitant fuzzy sets, respectively, Rodríguez et al. [30,31] investigated hesitant fuzzy linguistic term sets for decision making, Wei et al. [32] introduced some aggregation operators for hesitant fuzzy linguistic term sets and applied in multi-criteria decision making, Zhu et al. [33] introduced linguistic preference relation under hesitant fuzzy environment, Liao et al. [34,35] investigated distance and similarity measures between hesitant fuzzy linguistic term sets and the consistency and consensus of hesitant fuzzy preference relation, and applied in group decision making, Onar et al. [36] and Xu et al. [37] utilized hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution(TOPSIS) to obtain optimal strategy, respectively, Zhang et al. [38] investigated the extension of VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method based on hesitant fuzzy set(HFS), Qian et al. [39] proposed the generalized hesitant fuzzy set and applied in decision support system. ...
Weighted hesitant fuzzy set (WHFS) is an extension of hesitant fuzzy set (HFS), in which the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. In this paper, we redefine the union and intersection operations of weighted hesitant fuzzy elements (WHFEs), investigate their operation properties, and propose the variance function of the weighted hesitant fuzzy element (WHFE) to compare WHFEs. Furthermore, we develop two aggregation operators such as weighted hesitant fuzzy ordered weighted averaging (WHFOWA) and weighted hesitant fuzzy ordered weighted geometric (WHFOWG) operators to aggregate weighted hesitant fuzzy information, and present multiple-attribute group decision making algorithm under weighted hesitant fuzzy environment. Finally, four numerical examples are used to illustrate the effectiveness of our proposed aggregation operators.
... Following that, several innovative generalised versions of HFS are presented to effectively address ambiguity in real problems. Qian et al. 52 developed the generalise HFS, explored its arithmetic operations and relationships with the HFS, and eventually implemented it to practical MCDM. Zhu et al. 53 introduced dual HFS (DHFS) and analysed the basic operations and features while proposing a DHFS expansion concept. ...
... In Riera et al. (2015), a fuzzy decision-making model based on discrete fuzzy numbers is proposed for solving MCDM problems. In Qian et al. (2013), HFS is transformed into intuitionistic fuzzy sets and subsequently used to develop a decision support system for MCDM problems. Hesitant fuzzy linguistic Entropy and cross-entropy integrated with the queuing method is used to solve MCDM in Gou et al. (2017). ...
This paper introduces a new methodology for solving multi-attribute decision making (MADM) problems under hesitant fuzzy environment. The uncertainty in hesitant fuzzy elements (HFE) is derived by means of entropy. The resulting uncertainty is subsequently used in HFE to derive a single representative value (RV) of alternatives in each attribute. Our work transforms the RVs into their linguistic counterparts and then formulates a methodology for pairwise comparison of the alternatives via their linguistically defines RVs. The Eigen vector corresponding to maximum Eigen value of the pairwise comparison matrix prioritizes the alternatives in each attribute. The priority vectors of the alternatives are aggregated to derive the weights of the attributes using Quadratic programming. The weighted aggregation of the attribute values provides the ranking of the alternatives in MADM. An algorithm is written to validate the procedure developed. The proposed methodology is compared with similar existing methods, and the advantages of our method are presented. The robustness of our methodology is demonstrated through sensitivity analysis. To highlight the procedure, a car purchasing problem is illustrated.
... Generalized HFSs (Qian et al. [20]) Adopting an information system to stimulate university work productivity Chang [21] laid the foundation of "fuzzy topology", which is defined on a collection of fuzzy sets. Coker [22] proposed "intuitionistic fuzzy topology" which is defined on the collection of IFSs, and Olgun et al. [23] defined "Pythagorean fuzzy topology" on PFSs. ...
A hesitant fuzzy set (HFS) and a cubic set (CS) are two independent approaches to deal with hesitancy and vagueness simultaneously. An HFS assigns an essential hesitant grade to each object in the universe, whereas a CS deals with uncertain information in terms of fuzzy sets as well as interval-valued fuzzy sets. A cubic hesitant fuzzy set (CHFS) is a new computational intelligence approach that combines CS and HFS. The primary objective of this paper is to define topological structure of CHFSs under P(R)-order as well as to develop a new topological data analysis technique. For these objectives, we propose the concept of “cubic hesitant fuzzy topology (CHF topology)”, which is based on CHFSs with both P(R)-order. The idea of CHF points gives rise to the study of several properties of CHF topology, such as CHF closure, CHF exterior, CHF interior, CHF frontier, etc. We also define the notion of CHF subspace and CHF base in CHF topology and related results. We proposed two algorithms for extended cubic hesitant fuzzy TOPSIS and CHF topology method, respectively. The symmetry of optimal decision is analyzed by computations with both algorithms. A numerical analysis is illustrated to discuss similar medical diagnoses. We also discuss a case study of heart failure diagnosis based on CHF information and the modified TOPSIS approach.
... By using different fuzzy numbering approaches in the field of decision-making, MCDM aids in opting for the paramount decision. A few fuzzy numbering approaches are triangular fuzzy numbers (TFNs) [62,63], hesitant fuzzy numbers [64,65], trapezoidal fuzzy numbers [27,66], generalized fuzzy numbers (GFNs) [67], interval-valued triangular fuzzy numbers (IVTFNs) [68], intuitionistic fuzzy numbers [69] and linguistic fuzzy sets [70]. ...
Error due to human activities in any operation is analysed by using human reliability analysis approach in which the principal step is to identify the potential human errors followed by quantification and analysis of the error. The work presented in this research intends to apply a methodology for identifying human errors and to prioritize the risk associated with them in a LPG unloading operation. The methodology uses Hierarchical Task Analysis approach which provides the basic framework along with Systematic Human Error Reduction and Prediction Approach which aids in identification and categorization of the errors associated with each tasks with the help of predefined error taxonomy. Also, in order to quantify the risk associated with each identified error, fuzzy Failure Mode and Effect Analysis approach has been adopted. To rank and prioritize the risk associated with each identified errors where the individual constituent components are non-commensurable in nature, Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method has been incorporated. The applicability of the methodology presented will aid to comprehend the severity of risk corresponding to each error at different levels and the ranking mechanism thus developed in this work aids to prioritize the action to minimize the likelihood of errors.
... Following that, several innovative generalised versions of HFS are presented to effectively address ambiguity in real problems. Qian et al. 52 developed the generalise HFS, explored its arithmetic operations and relationships with the HFS, and eventually implemented it to practical MCDM. Zhu et al. 53 introduced dual HFS (DHFS) and analysed the basic operations and features while proposing a DHFS expansion concept. ...
Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q -rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q -rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method’s capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.
This research article proposes an innovative algorithm for analyzing parallelism in the evolution of hospital building features, with the goal of advancing decisionmaking processes in both urban and rural hospitals. As an additional generalization of the concepts of fuzzy sets, intuitionistic fuzzy sets, single-valued neutrosophic sets, hesitant fuzzy sets, and probabilistic fuzzy sets this paper proposes a single-valued neutrosophic probabilistic hesitant fuzzy set (SV-NPHFS). It is derived from the combination of single-valued neutrosophic sets, probabilistic fuzzy sets, and hesitant fuzzy sets. The novel algebraic structure and cosine evaluation function of SV-NPHFSs are then introduced. In addition, we introduce novel operators: the single-valued neutrosophic probabilistic hesitant fuzzy weighted geometric (SV-NPHFWG), the single-valued neutrosophic probabilistic hesitant fuzzy ordered weighted geometric (SV-NPHFOWG), the single-valued neutrosophic probabilistic hesitant fuzzy weighted average (SV-NPHFWA), and the single-valued neutrosophic probabilistic hesitant fuzzy ordered weighted average (SV-NPHFOWA). More complex links between features and alternatives can be made with the multi-attribute decision-making procedures outlined in this work. This characteristic highlights their superior practicality and accuracy over existing methods, which often fail to capture the intricate interplay of elements in real-world scenarios. This demonstrates that applying the decision-making strategies covered in this article can lead to the discovery of even additional trait correlations. Finally, we evaluate the performance of our proposed method on a real choice problem and an experimental comparison. The results demonstrate that the new method will be more advantageous in a range of applications where decision-making is uncertain. Figure 1 illustrates all of the manuscript?s results in a graphical abstract.
In this Chapter, the hybrid models known as multi-polar (m–polar) hesitant fuzzy sets, and hesitant m–polar fuzzy sets are presented. Both the presented models are the hybridization of hesitancy with m–polar fuzzy sets, and the natural generalization of hesitant fuzzy sets.
In a context marked by the rapid evolution of technologies and the omnipresence of IT at the heart of all activities, the digital transformation of companies is no longer a luxury but an absolute necessity. This technological transformation can lead to resistance from the employees affected by the change. In order to properly conduct the change management process, it is necessary to ensure the involvement of employees from the beginning of this process, which is composed of three phases: the change management strategy, the diagnosis, and the actions implementation. This paper focuses on the diagnostic phase and more specifically on the evaluation stage. This evaluation measures the employees’ hesitation to express their degree of resistance toward the digital initiatives launched in the company. However, this assessment is usually done subjectively, and employees express their hesitation in non-uniform manners. In this work, we propose a weighted generalized hesitating fuzzy approach based on the fusion of theoretical concepts of generalized hesitant fuzzy sets and formal concept analysis (FCA), to formalize the measurement of degree hesitation in change resistance. This approach is flexible and allows the top management of each organizational unit to correctly measure the resistance to change of their teams and then evaluate that measure at the global organizational level.
The Analytic Hierarchy Process (AHP) has been extensively utilized in multi-criteria decision making. Fuzzy sets have been widely employed to extend it under vagueness and impreciseness. Recent extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets, picture fuzzy sets, Pythagorean fuzzy sets, spherical fuzzy sets and neutrosophic sets have been employed to obtain the new versions of AHP under uncertainty. This chapter offers a concise overview of the literature on the integration of AHP with the extensions of ordinary fuzzy sets.
T-spherical fuzzy sets (T-SFSs) have fascinated the desire of researchers in a wide range of domains. The striking framework of the T-SFS is keen to offer the larger inclination domain for the modeling of ambiguous information deploying the degrees of membership, neutral and non-membership. Further, T-SFSs prevail over the theories of picture fuzzy sets, spherical fuzzy sets, and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being significant part of the literature, are crucial and beneficial tools that are widely applied in making decision, mining data, diagnosis of the medical things and recognition of the pattern. This paper aims to expand the literature on T-SFSs by introducing many innovative T-spherical fuzzy set information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for T-spherical fuzzy sets. Another achievement of this research is to establish a systematic transformation of information measures, measure distance, measure similarity, measure entropy, and measure inclusion for the T-SFSs. To accomplish this aim, new formula for information measure of T-SFSs have been provided. To demonstrate the criteria of the measures, we employ it to recognition pattern, building materials and diagnosis of the medical things. Additionally, a comparison between traditional and novel similarity measures is described in terms of counterintuitive cases. The outcomes demonstrate that the innovative information measures does not include any absurd cases.
Modern urban construction relies on a large number of projects. Project groups are an effective way to manage a large number of projects. In view of the current lack of scientific methods for constructing and evaluating project group programs, which are mainly based on subjective experience, this article proposes a scientific method for project group program generation and decision-making. The method proposed in this article applies a multi-layer coupling network to the modeling of project groups and divides projects into planning projects and execution projects to form a heterogeneous coupling network. Then, starting from the principle of project information dissemination, the evaluation indicators of the project group program were defined, and finally, the hesitant fuzzy decision-making method was used to assist in decision making. This article can provide a new method for project group construction and management, and provide strong support for the construction of smart cities and digital governments.
Hesitant and dual hesitant fuzzy sets are generalizations of fuzzy sets. Hesitant fuzzy sets (HFS) are the set of the membership grades only, while dual hesitant fuzzy sets (DHFS) are used to deal in real-life situations where we are in hesitant position to provide the satisfaction degree and dissatisfaction degree. The HFS and DHFS encompass fuzzy sets and intuitionistic fuzzy sets, respectively. In this paper, we introduce the concept of HFS and DHFS in the form of hesitant and dual hesitant fuzzy numbers (DHFNs) to compute the reliability of the optical fiber communication (OFC) system. The fuzzy Weibull distribution (FWD) and aggregation operators developed for the hesitant and dual hesitant fuzzy elements. The universal generating function (UGF) for HFS and DHFS are also developed in computing the fuzzy reliability. The UGF method has also been applied to find fuzzy reliability. To evaluate the fuzzy reliability for HFS and DHFS, \(\alpha -\)cut are used with different values of \(\alpha\).
The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.
Various companies have developed electric vehicle (EV)-based multiple fuel supply system modeling approaches (FSSMAs). Nonetheless, no superior approach concurrently satisfies all essential criteria, including ‘sustainability’ and ‘fuel consideration’ criteria. Furthermore, benchmarking the FSSMA alternatives to determine the most sustainable ones does not come without issues. The five main most common concerns are the use of various evaluation criteria, effecting the weights of the criteria with sublayers, criteria prioritization, trade-offs among the criteria, and data variations. Thus, this study proposes a novel FSSMA for EV benchmarking based on two methods—the Pythagorean probabilistic hesitant fuzzy sets and fuzzy weighted zero inconsistency (PPH–FWZIC) and the measurement of alternatives and ranking according to the compromise solution (MARCOS)—which are integrated as a single method. The PPM–FWZIC method was developed to solve the criteria prioritization issue, while the MARCOS method was developed to solve the various evaluation criteria, trade-offs among the criteria, and data variation issues to benchmark the FSSMA for EV alternatives. The integrated multicriteria decision-making (MCDM) method allows the system to perform a backward scoring process (BSP) and derive a scoring decision matrix from the formulated decision matrices that are performed based on the feed-forward data presentation (FFDP) procedure to solve the multiple criteria layers that affect the proper assessment of the impact of a certain criterion and its subcriteria in the weighting purpose issues. Subsequently, the FSSMAs for EVs are benchmarked, and the most sustainable approach is selected. The results were tested via sensitivity analysis and the Spearman correlation coefficient. The present study is also compared with a benchmark study based on a benchmarking checklist.
The paper presents a novel method of volumetric reconstruction of transient destructive processes using remote sensing by a group of unmanned aerial vehicles. The study is based on the most common class of such processes like forest fires, where a fire front is a determinant, and its propagation reflects the dynamics of the process. The effects of wind, smoke and fire, turbulence and vibration, interference, distortion, and obstacles lead to uncertainty of observations, to overcome which fuzzy sets, soft sets and gray numbers were combined. A spatial model based on a recursive eight-fold subdivision of space as well as on a hierarchical structure of virtual cells is proposed, which allowed to resolve the contradictions between the accuracy and rate of reconstruction. The set of possible states of virtual cells is determined and the algorithm of their classification based on the use of a five-channel image recognition system containing infrared, two main, and two additional optical channels is proposed. An algorithm for calculating a 3D observation vector, presented by an array of confidence vectors, is proposed, which can be used to determine the gray fuzzy state of virtual cells allowing a combination of observations from different observers and refining them sequentially. The terrain where the process evolves is represented by a soft gray fuzzy set of virtual cells, which belong to a specific state at the consideration time, allowing identification of convincing, uncertain, suspicious, and negative components. The first one defines a stable core of the fire front while the second one represents its variation caused by uncertainty. The proposed method allows the reconstruction of transient spatially distributed processes of other classes, smoothing the effects of distortions and noise and ensuring acceptable performance.
The consensus of randomness and ambiguity exists in real-world problems. To depict fuzziness, randomness, and statistical ambiguity in a single framework, the authors develop an interactive approach to MCDM method in which assessment of alternative over attributes are provided by probabilistichesitantfuzzyelements(PHFEs).Thismethodprovidesatooltothedecisionmakers forreasonablerankingofalternatives.Thecoreintentionofthispaperistodefineaseriesofnovel distanceandsimilaritymeasuresandscorefunctionforPHFEs.Todemonstratetheeffectiveness ofdevelopedmodel,arealcasestudyistakenasanexample.Tocompletelydescribestatisticaland non-statisticaluncertainty,suitableprobabilitydistributionfunctionisassociatedwitheachelementof constructedHFSs.TheproposedmethodissuperiortootherMCDMmethodsbecauseofintroducing probabilisticinformationinHFEs,whichcanbehelpfultoensuretheintegralityandaccurateness ofhesitantfuzzyinformation.
This study examines critical success factors (CSFs) for supply chain resilience regarding the selection of transportation service providers. Due to extensive global sourcing, many companies are dependent on multiple suppliers and service providers. Using a Delphi approach, this article identifies the CSFs relevant to the resilience of transportation service providers in supply chains. A novel approach using Multiple Criteria Decision-Analysis (MCDA) is then developed to rank a group of CSFs. In particular, the Best-Worst Method (BWM) and Multi-attributive Border Approximation Area Comparison (MABAC) methods are used to rank resilience-related CSFs for transportation service providers in uncertain environments using Hesitant Fuzzy Sets (HFS). Based on our results, hybrid MCDA methods can be applied in order to develop an effective method for determining resilience-related CSFs when selecting transportation service providers in uncertain environments.
In this study, the fusion of probabilistic hesitant fuzzy sets (PHFSs) and rough sets is explored and applied to uncertain multi-criteria decision-making (MCDM). First, to reduce the huge amount of computation of probabilistic hesitant fuzzy operations in the MCDM process, we introduce an advanced method to obtain normalized PHFSs (NPHFSs), in which each probabilistic hesitant fuzzy element (PHFE) has the same length and probability distribution. Second, based on NPHFSs, a novel probabilistic hesitant fuzzy rough set (PHFRS) model is established to solve the information aggregation problem in MCDM. Subsequently, we propose the concept of fuzziness of a PHFRS and develop a fuzziness-based objective weight determination method. Further, we construct an extended PROMETHEE II method based on a PHFRS for MCDM problems. Finally, we analyze the effectiveness of our proposed method through two MCDM problems along with experimental comparisons. The results illustrate that the proposed method is useful in numerous uncertain application fields.
This paper presents a method of relat-ing optimism and pessimism to multiple criteria decision analysis based on intuitionistic fuzzy sets. We develop the concepts of optimistic and pessimistic point operators to measure optimism and pessimism, respectively. Furthermore, we provide an approach to effectively capture the influences of optimism and pessimism on multiple criteria decision making. The suitability function is assessed according to the influence upon overall judgments or upon individual outcomes. Finally, we establish two algorithms to solve a multi-criteria decision making problem.
Predicting consumer sentiments revealed in online reviews is crucial to suppliers and potential consumers. We combine online sequential extreme learning machines (OS-ELMs) and intuitionistic fuzzy sets to predict consumer sentiments and propose a generalized ensemble learning scheme. The outputs of OS-ELMs are equivalently transformed into an intuitionistic fuzzy matrix. Then, predictions are made by fusing the degree of membership and non-membership concurrently. Moreover, we implement ELM, OS-ELM, and the proposed fusion scheme for Chinese reviews sentiment prediction. The experimental results have clearly shown the effectiveness of the proposed scheme and the strategy of weighting and order inducing.
A definition of the concept ‘intuitionistic fuzzy set’ (IFS) is given, the latter being a generalization of the concept ‘fuzzy set’ and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
Fuzzymultisets with infinitemembership sequences and their generalization using set-valued memberships are considered. Two
metric spaces of the infinite fuzzy multisets are defined in terms of cardinality. One is the completion of fuzzy multisets
of finite membership sequences; the other is derived from operations among fuzzy multisets and realvalued multisets. Theoretical
properties of these infinite fuzzy multisets are discussed.
To achieve consistent solutions is an important goal in group decision making problems. However, the expression of preferences is often a very difficult task for the experts, specially in decision problems with a high number of alternatives and when experts use fuzzy preference relations to provide their opinions. This usually leads to situations where experts are not able to properly express all their preferences in a consistent way, that is, without contradiction. In this paper, to overcome this problem, we present a decision support system based on consistency criteria to aid experts to express their fuzzy preference relations in a more consis-tent way. The system works interactively with the expert by providing him/her recommendations on the preference values that he/she has not yet expressed. These recommendations are computed trying to maintain the expert's consistency level as high as possible.
This paper presents a hybrid fuzzy model for group Multi Criteria Decision Making (MCDM). A modified fuzzy DEMATEL model is presented to deal with the influential relationship between the evaluation criteria. The modified DEMATEL captures such relationship and divides the criteria into two groups, particularly, the cause group and the effect group. The cause group has an influence on the effect group where such influence is used to estimate the criteria weights. In addition, a modified TOPSIS model is proposed to evaluate the criteria against each alternative. Here, a fuzzy distance measure is used in which the distance from the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) are calculated. The resulted distances were used to calculate the similarity to Ideal and Anti-ideal points. Later, an optimal membership degree (closeness coefficient) of each alternative is computed to estimate to which extent an alternative belongs to both FPIS and FNIS. The closer the degree of membership to FPIS and the farther from FNIS the more preferred the alternative. The membership degree is obtained by the optimization of a defined objective function that measures the degree to which an alternative is similar/dissimilar to the Ideal/Anti-Ideal solutions. The closeness coefficient is used to rank the alternatives. To better have a high contrast between the ranks of alternatives an optimization problem was introduced and solved to maximize the contrast.The presented hybrid model was applied on an industrial case study for the selection of cans supplier/suppliers at Nutridar Factory in Amman-Jordan to demonstrate the proposed model. Finally a sensitivity analysis is introduced to verify the resulting ranks of the available suppliers via testing different values of the used parameters. The sensitivity analysis has shown robust and valid results that are close to real preferences of the consulted experts.
Safety assessment of thermal power plants (TPP) is an important means to ensure the safety of production in thermal power production enterprises. Modern information technology can play an important role in TPP safety assessment. The evaluation of power plant systems relies, to a large extent, on the knowledge and experience of the experts undertaking the task. Case-based reasoning (CBR) is introduced for the safety assessment of TPP since it models expertise through experience management. This paper provides a case-based approach for the Management System safety assessment decision making of TPP (MSSATPP). We introduce a case matching method named CBR-Grey, which integrates the Delphi approach and grey system theory. Based on this method, we implement a prototype of case-based knowledge system (CBRSYS-TPP) for the evaluation decision making of the panel of experts. Our experimental results based on a real-world TPP safety assessment data set show that CBRSYS-TPP has high accuracy and systematically good performance.prs.rt("abs_end");KeywordsThermal power plants safety evaluation; Knowledge-based system; Case-based reasoning; Intelligent decision support system; Grey system theoryFigures and tables from this article:Fig. 1. Evaluation indexes and four extra output attributes in IDSS-TPP.Figure optionsView in workspaceTable 1.
Kendall’s W test result.
Game theory has been applied extensively to interpret and solve the complex and interrelated practical decision problems. The solution for these problems depends on the goals pursued by different interested parties, i.e., problems as conflict situations. Decision making approaches based on game theory have been an important and promising research direction in decision science, as well as in real-world practice. Many research approaches within this direction have been developed, but most are limited to the real-valued domain. A great amount of non-real valued domain practical game decision problems, especially the lattice-valued game, remain largely unexplored. This paper investigates the lattice-valued matrix game (including the real-valued matrix game as a special case). For decision purposes, it is an essential and indispensable step in theoretical game decision approaches to find the solutions for a matrix game; hence this work focuses on how to determine solutions of lattice-valued matrix game for decision purposes. Firstly, based on the work on lattice-valued matrix game with pure strategy, a concept of multi-dimension lattice-valued-level strategy is introduced based on a new algebra structure called the l∗-module, i.e., a lattice-ordered module with two lattice-ordered structures. Next, a concept of a mixed strategy lattice-valued matrix game is introduced and its basic properties are discussed. Finally, the necessary and sufficient condition for the existence of a solution for a mixed strategy lattice-valued matrix game is discussed, along with basic properties for the solution. The approaches and results discussed are mathematical in nature and entail fundamental research in the field of intelligent decision support. They will provide important and fundamental support for the application of a theoretical game approach in rational decisions for conflict situations, and also introduce a new branch of game-theory based decision approaches by extending real-valued game theory into lattice-value game theory.
With the ever increasing public awareness of complicated road safety phenomenon, much more detailed aspects of crash and injury causation rather than only crash data are extensively investigated in the current road safety research. Safety performance indicators (SPIs), which are causally related to the number of crashes or to the injury consequences of a crash, are rapidly developed and increasingly used. To measure the multi-dimensional concept of road safety which cannot be captured by a single indicator, the exploration of a composite road safety performance index is vital for rational decision-making about road safety. In doing so, a proper decision support system is required. In this study, we propose an improved hierarchical fuzzy TOPSIS model to combine the multilayer SPIs into one overall index by incorporating experts’ knowledge. Using the number of road fatalities per million inhabitants as a relevant reference, the proposed model provides with a promising intelligent decision support system to evaluate the road safety performance for a case study of a given set of European countries. It effectively handles experts’ linguistic expressions and takes the layered hierarchy of the indicators into account. The comparison results with those from the original hierarchical fuzzy TOPSIS model further verify the robustness of the proposed model, and imply the feasibility of applying this model to a great number of performance evaluation and decision making activities in other wide ranging fields as well.
Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a suitable means
allowing several possible degrees for an element to a set. In this paper, we study the aggregation of the hesitancy fuzzy
information. Several series of aggregation operators are proposed and the connections of them are discussed. To reflect the
correlation of the aggregation arguments, two methods are proposed to determine the aggregation weight vectors. Based on the
support degrees among aggregation arguments, the weight vector of decision makers are obtained more objectively. To deal with
the correlation of criteria, we apply the Choquet integral to get the weights of criteria. A method is also proposed for group
decision making under hesitant fuzzy environment.
The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.
A vague set is a set of objects, each of which has a grade of
membership whose value is a continuous subinterval of [0,1]. Such a set
is characterized by a truth-membership function and a false-membership
function. The notion of inclusion, union, intersection, and complement
are extended to such sets, and various properties of vague sets are
established. Finally, convex vague sets are introduced
The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Interval-valued fuzzy sets have been developed and applied to multiple criteria analysis. However, the influence of optimism and pessimism on subjective judgments and the cognitive dissonance that accompanies the decision making process have not been studied thoroughly. This paper presents a new method to reduce cognitive dissonance and to relate optimism and pessimism in multiple criteria decision analysis in an interval-valued fuzzy decision environment. We utilized optimistic and pessimistic point operators to measure the effects of optimism and pessimism, respectively, and further determined a suitability function through weighted score functions. Considering the two objectives of maximal suitability and dissonance reduction, several optimization models were constructed to obtain the optimal weights for the criteria and to determine the corresponding degree of suitability for alternative rankings. Finally, an empirical study was conducted to validate the feasibility and applicability of the current method. We anticipate that the proposed method can provide insight on the influences of optimism, pessimism, and cognitive dissonance in decision analysis studies.
Multi-criteria group decision making (MCGDM) aims to support preference-based decision over the available alternatives that are characterized by multiple criteria in a group. To increase the level of overall satisfaction for the final decision across the group and deal with uncertainty in decision process, a fuzzy MCGDM process (FMP) model is established in this study. This FMP model can also aggregate both subjective and objective information under multi-level hierarchies of criteria and evaluators. Based on the FMP model, a fuzzy MCGDM decision support system (called Decider) is developed, which can handle information expressed in linguistic terms, boolean values, as well as numeric values to assess and rank a set of alternatives within a group of decision makers. Real applications indicate that the presented FMP model and the Decider software are able to effectively handle fuzziness in both subjective and objective information and support group decision-making under multi-level criteria with a higher level of satisfaction by decision makers.
As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an element to a set caused by a doubt between a few different values. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy information. We first discuss the relationship between intutionistic fuzzy set and hesitant fuzzy set, based on which we develop some operations and aggregation operators for hesitant fuzzy elements. The correlations among the aggregation operators are further discussed. Finally, we give their application in solving decision making problems.
For the real decision making problems, most criteria have inter-dependent or interactive characteristics so that it is not suitable for us to aggregate them by traditional aggregation operators based on additive measures. Thus, to approximate the human subjective decision making process, it would be more suitable to apply fuzzy measures, where it is not necessary to assume additivity and independence among decision making criteria. In this paper, an intuitionistic fuzzy Choquet integral is proposed for multiple criteria decision making, where interactions phenomena among the decision making criteria are considered. First, we introduced two operational laws on intuitionistic fuzzy values. Then, based on these operational laws, intuitionistic fuzzy Choquet integral operator is proposed. Moreover, some of its properties are investigated. It is shown that the intuitionistic fuzzy Choquet integral operator can be represented by some special t-norms and t-conorms, and it is also a generalization of the intuitionistic fuzzy OWA operator and intuitionistic fuzzy weighted averaging operator. Further, the procedure and algorithm of multi-criteria decision making based on intuitionistic fuzzy Choquet integral operator is given under uncertain environment. Finally, a practical example is provided to illustrate the developed approaches.
Detecting logical inconsistency in collected information is a vital function when deploying a knowledge-based warning system to monitor a specific application domain for the reason that logical inconsistency is often hidden from seemingly consistent information and may lead to unexpected results. Existing logical inconsistency detection methods usually focus on information stored in a knowledge base by using a well-defined general purpose knowledge representation approach, and therefore cannot fulfill the demands of a domain-specific situation. This paper first proposes a state-based knowledge representation approach, in which domain-specific knowledge is expressed by combinations of the relevant objects’ states. Based on this approach, a method for information logical inconsistency detection (ILID) is developed which can flexibly handle the demands of various domain-specific situations through reducing part of restrictions in existing methods. Finally, two real-case based examples are presented to illustrate the ILID method and its advantages.
In this paper, a new method for handling multicriteria fuzzy decision-making problems based on intuitionistic fuzzy sets is presented. The proposed method allows the degrees of satisfiability and non-satisfiability of each alternative with respect to a set of criteria to be represented by intuitionistic fuzzy sets, respectively. Furthermore, the proposed method allows the decision-maker to assign the degrees of membership and non-membership of the criteria to the fuzzy concept “importance.” The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision.
In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.
We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster–Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster–Shafer operators. Then we investigate their various properties and some of their special cases. Additionally, we apply the developed operators to financial decision making under intuitionistic fuzzy environments. Some extensions in interval-valued intuitionistic fuzzy situations are also pointed out.
Information axiom, one of two axioms of axiomatic design methodology which is proposed to improve a design, is used to select the best design among proposed designs. In the literature, there are a lot of studies related to using of information axiom for the solution of decision making problems. Moreover, applications of information axiom have been increasing day by day. However, calculation procedure of information axiom is not only incommodious but also difficult for decision makers. In this paper, a decision support system (DSS) based on fuzzy information axiom (FIA) is developed in order to make this decision procedure easy. The developed system consists of a knowledge base module including facts and rules, inference engine module including FIA and aggregation method, and a user interface module including entrance windows. The main aim of this study is to present a DSS tool to help the decision makers to solve their decision problems by modifying data-base of the program. In this paper, an application procedure will be presented based on the optimal selection of location for emergency service to illustrate the implementation procedure of the proposed model.
New techniques for handling multicriteria fuzzy decision-making problems based on vague set theory are presented. The proposed techniques allow the degrees of satisfiability and non-satisfiability of each alternative with respect to a set of criteria to be presented by vague values. Furthermore, the proposed techniques allow the decision-maker to assign a different degree of importance to each criteria. The techniques proposed in this paper can provide a useful way to efficiently help the decision-maker to make his decisions.
We recapitulate the definition given by Atanassov (1983) of intuitionistic fuzzy sets as well as the definition of vague sets given by Gau and Byehrer (1993) and see that both definitions coincide.
The concept of fuzzy sets of type 2 has been defined by L. A. Zadeh as an extension of ordinary fuzzy sets. The fuzzy set of type 2 can be characterized by a fuzzy membership function the grade (or fuzzy grade) of which is a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1].This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊔, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzy grades form a distributive lattice under ⊔ and ⊓. Moreover, the algebraic properties of fuzzy grades under the operations and which are slightly different from ⊔ and ⊓, respectively, are briefly discussed.
A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Decisions in a decentralized organization often involve two levels. The leader at the upper level attempts to optimize his/her objective but is affected by the follower; the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. When model a real-world bilevel decision problem, it also may involve fuzzy demands which appear either in the parameters of objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict objectives that should be optimized simultaneously in achieving a solution. This study addresses both fuzzy demands and multi-objective issues and propose a fuzzy multi-objective bilevel programming model. It then develops an approximation branch-and-bound algorithm to solve multi-objective bilevel decision problems with fuzzy demands. Finally, two case-based examples further illustrate the proposed model and algorithm.
Multiple criteria decision making (MCDM) is widely used in ranking one or more alternatives from a set of available alternatives with respect to multiple criteria. Inspired by MCDM to systematically evaluate alternatives under various criteria, we propose a new fuzzy TOPSIS for evaluating alternatives by integrating using subjective and objective weights. Most MCDM approaches consider only decision maker’s subjective weights. However, the end-user attitude can be a key factor. We propose a novel approach that involves end-user into the whole decision making process. In this proposed approach, the subjective weights assigned by decision makers (DM) are normalized into a comparable scale. In addition, we also adopt end-user ratings as an objective weight based on Shannon’s entropy theory. A closeness coefficient is defined to determine the ranking order of alternatives by calculating the distances to both ideal and negative-ideal solutions. A case study is performed showing how the propose method can be used for a software outsourcing problem. With our method, we provide decision makers more information to make more subtle decisions.
Intuitionistic fuzzy sets (IFS) are a generalization of fuzzy sets where the membership is an interval. That is, membership, instead of being a single value, is an interval. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. In this paper we describe hesitant fuzzy sets. They are another generalization of fuzzy sets. Although similar in intention to IFS, some basic differences on their interpretation and on their operators exist. In this paper we review their definition, the main results and we present an extension principle, which permits to generalize existing operations on fuzzy sets to this new type of fuzzy sets. We also discuss their use in decision making.
Many multiple attribute decision analysis (MADA) problems are characterized by both quantitative and qualitative attributes with various types of uncertainties. Incompleteness (or ignorance) and vagueness (or fuzziness) are among the most com- mon uncertainties in decision analysis. The evidential reasoning (ER) and the interval grade ER (IER) approaches have been de- veloped in recent years to support the solution of MADA problems with interval uncertainties and local ignorance in decision analy- sis. In this paper, the ER approach is enhanced to deal with both interval uncertainty and fuzzy beliefs in assessing alternatives on an attribute. In this newly developed fuzzy IER (FIER) approach, local ignorance and grade fuzziness are modeled under the inte- grated framework of a distributed fuzzy belief structure, leading to a fuzzy belief decision matrix. A numerical example is provided to illustrate the detailed implementation process of the FIER ap- proach and its validity and applicability.
Nowadays, stock market is becoming a popular investment platform for both institutional and individual investors. The current financial information systems serve to provide latest information. However, they lack sophisticated analytical tools. This paper proposes a new architecture for financial information systems. The developed prototype is entitled as the Multi-level and Interactive Stock Market Investment System (MISMIS). It is specially designed for investors to build their financial models to forecast stock price and index. The performance of the financial models can be evaluated on a virtual trading platform. There are other features in MISMIS that are tailor-made to handle financial data; these include synchronized time frame, time series prediction techniques, preprocessing and transformation functions, multi-level modeling and interactive user interface. To illustrate the capability of MISMIS, we have evaluated strategies of trading the future options of Hang Seng Index (HSI). We find that historical HSI, Dow Jones Index, property price index, retailing sales figure, prime lending rate, and consumer price index in Hong Kong are essential factors affecting the performance of the trading of HSI’s future option. Also there are some feedbacks from the in-depth interviews of six financial consultant upon how they perceived the prototype MISMIS.
This paper proposes a series of aggregation operators considering the confidence levels of the aggregated arguments. Due to the complex connections among the arguments, we further give two nonlinear aggregation operators and discuss their properties. Then we extend these aggregation operators to hesitant fuzzy environments in which there are some difficulties in determining the membership of an element to a set. Several numerical examples are used to compare the proposed aggregation operators.
Aggregation of intuitionistic fuzzy information is a new branch of intuitionistic fuzzy set theory, which has attracted significant
interest from researchers in recent years. In this paper, we provide a survey of the aggregation techniques of intuitionistic
fuzzy information, and their applications in various fields, such as decision making, cluster analysis, medical diagnosis,
forecasting, and manufacturing grid. In addition, we analyze their characteristics and relationships. Finally, we discuss
possible directions for future research in this area.
In this work, we first make a survey of the existing main aggregation operators and then propose some new aggregation operators such as the induced ordered weighted geometric averaging (IOWGA) operator, generalized induced ordered weighted averaging (GIOWA) operator, hybrid weighted averaging (HWA) operator, etc., and study their desirable properties. Finally, we briefly classify all of these aggregation operators. © 2003 Wiley Periodicals, Inc.
Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.
Yager (Fuzzy Sets, Syst 2003;137:59–69) extended the idea of order-induced aggregation to the Choquet aggregation and defined induced Choquet ordered averaging operator. In this paper, an induced intuitionistic fuzzy Choquet (IFC) integral operator is proposed for the multiple criteria decision making. Some of its properties are investigated. Furthermore, an induced generalized IFC integral operator is introduced. It is worth mentioning that most of the existing intuitionistic fuzzy aggregation operators are special cases of this induced aggregation operator. A decision procedure based on the proposed induced aggregation operator is developed for solving the multicriteria decision-making problem in which all the decision information is represented by intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.
A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express people's hesitancy in daily life. In this paper, we define the distance and correlation measures for hesitant fuzzy information and then discuss their properties in detail. These measures are all defined under the assumption that the values in all hesitant fuzzy elements (the fundamental units of hesitant fuzzy sets) are arranged in an increasing order and two hesitant fuzzy elements have the same length when we compare them. We can find that the results, by using the developed distance measures, are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations. In addition, the derived correlation coefficients are based on different linear relationships and may have different results. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.
The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval-valued intuitionistic fuzzy weighted averaging operator, generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval-valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval-valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.
Skin keratinocytes express tissue factor (TF) and are highly associated with skin wound healing. Although it has been demonstrated that perivascular TF expression in granulation tissue formed after dermal injury is downregulated during healing, studies of the mechanism of factor (F) VII, a TF ligand, in skin wound healing are lacking. We reported the use of a dermal punch model to demonstrate that low-expressing FVII mice (approximately 1% of wild type [WT]) exhibited impaired skin wound healing compared with WT controls. These low-FVII mice showed defective reepithelialization and reduced inflammatory cell infiltration at wound sites. This attenuated reepithelialization was associated with diminished expression of the transcription factor early growth response 1 (Egr-1). In vitro, Egr-1 was shown to be essential for the FVIIa-induced regulation of keratinocyte migration and inflammation. Both Egr-1 upregulation and downstream inflammatory cytokine appearance in keratinocytes depended on FVIIa/TF/protease-activated receptor 2 (PAR-2)-induced signaling and did not require subsequent generation of FXa and thrombin. The participation of Egr-1 in FVIIa-mediated regulation of keratinocyte function was confirmed by use of Egr-1-deficient mice, wherein a significant delay in skin wound healing after injury was observed, relative to WT mice. The results from these studies demonstrate an in vivo mechanistic relationship between FVIIa, Egr-1 and the inflammatory response in keratinocyte function during the wound healing process.
An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
Optimism and pessimism in decision making based on intuitionistic fuzzy sets
- T Y Chen
- C W Tsui
T.Y. Chen, C.W. Tsui, Optimism and pessimism in decision making based on
intuitionistic fuzzy sets, in: Proceedings of the 11th Joint Conference on
Information Sciences, 2008.
Vague sets are intuitionistic fuzzy sets
- Bustince