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Extended fuzzy cognitive maps
Abstract
Fuzzy cognitive maps (FCMs) have been proposed to represent causal
reasoning by using numeric processing. They graphically represent
uncertain causal reasoning. In the resonant states, there emerges a
limit cycle or a hidden pattern, which is a FCM inference. However,
there are some shortcomings concerned with knowledge representation in
the conventional FCMs. The author proposes extended fuzzy cognitive maps
(E-FCMs) to represent causal relationships more naturally. The features
of the E-FCMs are nonlinear membership functions, conditional weights,
and time delay weights. Computer simulation results indicate the
effectiveness of the E-FCMs
... If modelers have a given use case in mind and are unsure what additional capabilities they need, we suggest they use Fig. 6 [ 22], Unsupervised Dynamic FCM (UDFCM) [ 9], Generalized Logistic Function (GLF) [ 8], Time-Delay Mining Fuzzy Time Cognitive Map (TM-FTCM) [ 6], Intuitionistic FCM (iFCM-II) [ 14], Extended-FCM (E-FCM) [ 3], Neutrosophic Cognitive Map (NCM) Extension [ 1,7], Fuzzy Grey Cognitive Maps (FGCM) [ 17], Interval-Valued FCM (IVFCM) [ 5], FCM for Discrete Random Variables (FCM4DRV) [ 20], Time-Interval FCM (TI-FCM) [ 11], Ensemble IVFCM [ 21], and High-Order Intuitionistic FCM (IFCMR) [ 23] extensions applied to it. Then, they can use Fig. 6.2 to identify additional features and needs of each extension to select one that they have the resources to implement (either participants or data) with the most appropriate added features. ...
... Extended-FCMs (E-FCMs) address these three limitations [ 3] by replacing crisp weights of the FCM with weight functions and introducing time delays. The E-FCM construction process closely resembles the FCM's, but participants must identify if the relationship is nonlinear, delayed, or conditional. ...
... Second, recent extensions have focused on specific application domains and use cases, whereas more established extensions sought to be broadly applicable. For example, the E-FCM [ 3], proposed in 1992, was designed to allow the FCM to represent nonlinearity, time delays/lags, and conditional weights without a specific application domain in mind, whereas the DFCM [ 22] (published in 2020) focuses on multivariate time series forecasting. The more specific a model is, the better it may perform for the desired use case; however, its use cases are more limited. ...
Fuzzy Cognitive Maps (FCMs) are interpretable simulation models capable of representing complex systems; however, they have numerous limitations. They can only represent causal relationships, have a limited representation of uncertainty, and cannot capture nonlinear relationships, time delays/lags, or conditional relationships. Thus, several extensions of FCMs have been proposed. We organize various use cases, additional features, and added requirements of extensions of FCMs and identify candidates to support extension selection given a particular scenario. We examine how to build Interval-Valued FCMs (IVFCMs), Time-Interval FCMs (TI-FCMs), and Extended-FCMs (E-FCMs), how they operate, and the additional features they offer to introduce a subset of extensions. We comment on three trends of applying and developing extensions and suggest two skills for modelers to effectively use extensions. Finally, we provide exercises to solidify the readers’ understanding of extensions. After reading this chapter and completing its problems, readers should understand why we extend FCMs and be able to compare extensions and their additional capabilities. Moreover, they should be able to select and apply an extension for numerous distinct use cases.
... In an NCM, each edge weight is in the set {−1 , 0 , 1 , I } where I represents indeterminacy. This example is derived from [ 26 ]. Given the ease to construct and interpret FCMs as well as their flexibility to simulate complex systems, this method was noted in over 20,000 scientific papers [ 34 ]. ...
... Although FCMs are a popular and powerful tool for modeling complex systems, they have several limitations. In 1992, Hagiwara focused on three such limitations [ 26 ]. First, weights can only be linear. ...
... For brevity, the mathematical characteristics of these extensions are summarized in Table A.1 . As stated in the introduction, a prominent extension was created by Hagiwara to introduce (i) weights with nonlinear membership functions; (ii) the notion of time, particularly, delays on weights; and (iii) conditional weights [ 26 ]. In this Extended Fuzzy Cognitive Map (E-FCM) ( Figure 5 (a)), the total input to a node C j at a time t (see Equations ( 1 ) and ( 2 )) can be expressed as ...
Fuzzy Cognitive Maps (FCMs) are widely used to simulate complex systems. However, they cannot handle nonlinear relationships, time delays/lags, or fully represent uncertain information, which prompted the development of extended FCMs. The latest review covered extensions up to 2010. We search for extensions from 2011 to March 2023 and assess their motivations, features, operationalizations, use cases, reproducibility, and evaluation to support modelers in reusing existing solutions. We reviewed 26 extensions and found a paucity of extensions addressing multiple limitations, and none of the extensions provided code, hindering modelers in reusing existing extensions while suggesting future work.
... Both numeric and linguistic models may be applied in this context [4,6]. However, the extended time inclusive approach is still quite rarely adopted within the FCMs even though it plays an important role particularly when organizational design aspects are involved in these systems [4,18,21]. ...
... Not all systems have already such a refined quantitative knowledge to estimate whether their cause-effect relations are delayed or immediate. When the behavioral pattern of the system is unknown, application of temporal factors in FCM calculations allows experts to discover this pattern, throwing new light on their system's understanding and time span calibration [10,18,[20][21][22]. ...
... As described in [17], sense-making is an action which involves turning circumstances into a situation that is comprehended explicitly in words or speech and that serves as a springboard to action. In [18], in turn, was noticed that research and theory on organizations are lacking a critical specification on time scale. Specification of the relevant time scale is as critical as the specification of the appropriate level or unit of analysis, a concept to which it is related. ...
... As a result, it is necessary to suggest some modifications to the basic structure of FMC. In order to overcome problems of the basic FMC, such as a linearity, first-order dynamics, a lack of time delay and an inability to represent logical operators, the following already established extensions can be taken into consideration (see Fig. 3) [12]: ...
... Our proposal is motivated mainly by the Extended Fuzzy Cognitive Maps (E-FCMs -see Fig. 3) [12] by Hagiwara, but our approach is different and more general. The E-FCMs tackle the problems of the conventional FCMs by adding support for nonlinear relations, conditional relations and time delayed relations. ...
... A visualization of the concept relations within the FCM model of a city. It is clearly visible, that the relations can be represented only as linear functions[12]. ...
In this paper, we propose a novel approach to modeling using fuzzy cognitive maps, which we refer to as the Three-Term Relation Neuro-Fuzzy Cognitive Map or simply the TTR NFCM. The proposed method is mostly suited to model complex nonlinear technical systems with dynamic internal characteristics. With this method we aim to solve some of the most critical problems of the conventional fuzzy cognitive maps. We target two of these problems by hybridization with artificial neural networks. First of them is a linear nature of relations between the concepts. The second is a lack of mutual dependence between the relations connecting to the same concept. Finally, we tackle a problem of relation dynamics using an inspiration from the control engineering. While focusing on bringing these advanced additional methods to the design of cognitive maps, we also aim to keep the degree of dependency on expert knowledge on the same level as with the conventional fuzzy cognitive maps. We achieve this by utilizing the machine learning methods. However, since the proposed method is heavily dependent on automated data-driven learning, it is suitable mainly for systems which are well observable and can produce sufficient training datasets.
... Fuzzy cognitive maps have been studied and used in various fields of engineering and hard sciences [2]. Their role is especially important in investigations of the behavior of complex dynamic systems [3], [4], [5], [6]. This is due to the fact that human knowledge uncertainty affects the systems definition and processing [7]. ...
... We mark such weight matrix members with the minus sign. Sets of generators of the lattice elements, including such weights in the join, will be deducted from the join by (3). Thus, we consider the following weight matrix corresponding to the similar one of [20] and Table 1: Table 7. ...
A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an ap- proach allows us to operate in cognitive maps with partially-ordered linguis- tic variables directly, without vague fuzzification/defuzzification methods. Hence, we may consider more subtle differences in degrees of experts' uncer- tainty, than in the fuzzy case. We prove the convergence of such cognitive maps and give a simple computational example which demonstrates using such a partially-ordered uncertainty degree scale.
... Extended FCMs (E-FCMs) was proposed by Hagiwara [43], and is the first advance in FCMs to include time relations. The capture of time relations are not detailed, however, time in E-FCMs are represented explicitly using fuzzy rules and modelled using static delays. ...
... The conventional implementation of a delay in FCMs [43,48] is modelled using the following equation ...
Fuzzy Cognitive Maps (FCMs) have been used to quantitatively model the dynamics of complex systems and predict their behaviours. However, they are usually unable to address the issues arising from time lags between causes and effects. Accordingly, Generalized Fuzzy Cognitive Maps (GFCMs) have been introduced to overcome this problem. This article deals with a breed of GFCMs that addresses time lags between cause(s) and effect(s), demonstrated by a case-study that deals with the social, economic and technological consequences of heavy rainfall in Kampala, Uganda. The results show that the inclusion of time lags alters both, the final steady-state values of the social, economic and technological consequences of heavy rainfall and the time taken to stabilise. Thus, the inclusion of time lags increases the reliability of GFCMs as a means to quantitatively model the dynamics of complex systems.
... The conventional implementation of a delay in FCMs [63,79] is modelled using the following equation ...
... This is done by representing complex causal relations as fuzzy If-Then rules (see Section 3.2.2). Several FCMs extensions [34,38,63,64] use fuzzy rules to try to separate the notion of a concept from a node. Most studies that include fuzzy rules for the representation of concepts and their interaction within the system invariably de-fuzzify (Equation 3.8) their results because classical fuzzy arithmetics' is not supported in the conventional FCMs approaches (see Equation 2.1). ...
... Two main approaches have been developed to overcome the information gap. Imprecision of information, resulting in the acceptance of subjective assessments, is taken into account by introducing fuzzy inference [2], [3], [6], [9]. Lack of full information is compensated by the use of various techniques of computational intelligence, mainly based on a digraph structure, such as artificial neural networks and cognitive maps. ...
... Lack of full information is compensated by the use of various techniques of computational intelligence, mainly based on a digraph structure, such as artificial neural networks and cognitive maps. The special role is played by (so-called) Fuzzy Cognitive Maps (FCM), e. g. [3], [6], [10], [11], [15], that are used in many areas of subjective inference. In addition to classical types, there are other FCM models, e.g.: Intuitionistic FCMs [14], Interval-Valued FCMs [7] or Competitive FCMs [1]. ...
During the modeling of uncertain and imprecise systems, the intelligent approach, based on the use of so-called Fuzzy Cognitive Maps (FCM) is often used. Constructors of the FCM models usually use a technique, in which fuzzy quantities are converted to their crisp equivalents (e.g. in a model learning phase). Such a procedure converts the fuzzy model in a crisp model, which may be a problem in systems with uncertainty. This risk can be avoided by building a model based on fuzzy numbers, fuzzy relations and fuzzy arithmetic operations, but then the new problem – of technical nature – arises, related to the specifics of operations on fuzzy numbers – manifested in the support deformations. The paper proposes a solution to this problem, consisting in a new look at the interpretation of the results of arithmetic operations on fuzzy numbers. New mechanism, that allows overcoming the negative effects of such deformations, is presented. The use of the proposed approach enables maintaining the fuzzy nature of the model at each stage of its operation. The results of simulations for different variants of the proposed method are also shown.
... FCM have been introduced by Kosko [3,4], who enhanced the cognitive maps theory that had been used in social and political sciences to analyze social decision-making problems; showing a causal relationship between different factors, where the causal relationship is expressed by either positive or negative sign of knowledge expression [5]. Fuzzy values introduced in cognitive maps and FCM were used to represent causal reasoning [6]. FCM have been used to provide decision analysis and cooperation among distributed agents [7], to model Medical Decision Support Systems [8], and have been accompanied with case-based reasoning approaches [9]. ...
... Thus, neuro-fuzzy systems with their ability to incorporate human knowledge and to adapt their knowledge base via new optimization techniques are likely to play increasingly important roles in the conception and design of hybrid intelligent systems [24]. Each FCM developed is a conceptual network, which is built by experts, using an interactive procedure of knowledge acquisition [6]. ...
The power market is becoming more complex as independent small producers are entering it, but their energy offerings are often based on alternative sources which may be dependent on transient weather conditions. Power market auction behavior is a typical large-scale system characterized by huge amounts of data and information that have to be taken into consideration to make decisions. Fuzzy Cognitive Maps (FCM) offer a method for using the knowledge and experience of domain experts to describe the behavior of a complex system. This paper discusses FCM representation and development, and describes the use of FCM to develop a behavioral model of the system. This paper then presents the soft computing approach of FCM for modeling complex power market behavior. The resulting FCM models a variety of factors that affect individual participant behaviors during power auctions and provides an abstract conceptual model of the interacting entities for a specific case problem.
... Hagiwara [26] was the first researcher to acknowledge the lack of the concept of time in FCMs, along with the need for conditional and non-linear causal relationships; he therefore proposed an extended FCM framework that is able to incorporate time delays, non-linear weights and conditional relations. However, this approach not only requires an extensive, time-consuming stakeholder engagement framework that assumes experts' knowledge and expertise is adequate for offering insight into all of the required information, but also significantly enhances the complexity of the FCM methodology. ...
... Other approaches include the expression of the implicit time delay of every relation and the selection of a base time in Rule-Based Fuzzy Cognitive Maps [15]; the use of Fuzzy Time Cognitive Maps for analyzing trust dynamics in virtual enterprises [74]; the agent-based FCM methodological framework developed by Lee et al. [44], in an effort to better address the drawbacks identified by Hagiwara [26] and further analyzed by Schneider et al. [60], which was applied in industrial marketing planning; and a significantly more complex version of timed fuzzy cognitive maps that requires the determination of linguistically-expressed time-dependent weights [10]. ...
Climate change has been considered one of the most significant risks for sustainability in our century; in order to move towards low-carbon and climate resilient economies, fundamental changes must take place. In this direction, the European Union has set ambitious goals regarding the transition of its Member States to low carbon societies, but the policy strategies to promote this transition must be socially acceptable and supported. So far, climate policies have been evaluated using quantitative methods, including general equilibrium and integrated assessment models but, despite their undoubted contribution to climate modeling, both the quantitative frameworks used for studying climate change and its impacts and those aiming at policy optimization or evaluation feature significant uncertainties and limitations. In order to overcome these issues, a Fuzzy Cognitive Map based approach is proposed, aiming to directly involve stakeholders and assess human knowledge and expertise. The suggested methodological framework can significantly support climate policy making, by supplementing quantitative models and exploring impacts of selected sets of policies, based on qualitative information deriving from a structured stakeholder engagement process. Finally, an innovative approach of incorporating the concept of time into the methodology is proposed and evaluated, in the aim of enhancing the robustness of transition pathways.
... The literature is rich with noteworthy research publications, contributing to the continuous evolution of cognitive maps. Hagiwara's work delved into non-linear causality in arcs [4], Carvalho and Tomé explored rule-based FCMs [5], Khor ventured into fuzzy knowledge maps [6], and Augustine et al. introduced rate cognitive maps for failure mode identification [7]. As the field advanced, new variants emerged, such as Salmeron's fuzzy grey cognitive maps [8], Cai et al.'s evolutionary fuzzy cognitive maps [9], Iakovidis and Papageorgiou's intuitionistic fuzzy cognitive maps [10], Ruan et al.'s belief degree-distributed fuzzy cognitive maps [11], and Chunying et al.'s rough cognitive maps [12]. ...
Fuzzy cognitive maps (FCMs) provide a rapid and efficient approach for system modeling and simulation. The literature demonstrates numerous successful applications of FCMs in identifying failure modes. The standard process of failure mode identification using FCMs involves monitoring crucial concept/node values for excesses. Threshold functions are used to limit the value of nodes within a pre-specified range, which is usually [0, 1] or [-1, + 1]. However, traditional FCMs using the tanh threshold function possess two crucial drawbacks for this particular.Purpose(i) a tendency to reduce the values of state vector components, and (ii) the potential inability to reach a limit state with clearly identifiable failure states. The reason for this is the inherent mathematical nature of the tanh function in being asymptotic to the horizontal line demarcating the edge of the specified range. To overcome these limitations, this paper introduces a novel modified tanh threshold function that effectively addresses both issues.
... Outras variações dos Mapas Cognitivos Fuzzy que se preocupam com a representação rígida do conhecimento são conhecidas na literatura: E-FCM (Extended-Fuzzy Cognitive Maps) (Hagiwara, 1992), RB-FCM (Rule Based Fuzzy Cognitive Maps) (Carvalho and Tome, 2000), DCN (Dynamic Cognitive Network ) (Kostiadis et al., 2000) e (Miao et al., 2010) Todos os pesos em ambos HD-FCM são ajustados heuristicamente de forma off-line da seguinte forma: após a determinação do sinal causal, os valores dos pesos foram inicializados em +0,5 ou -0,5 (dependendo da causalidade entre os conceitos). Esses pesos iniciais para os HD-FCMs são mostrados nas matrizes 3 e 4. Após esta etapa, observando-se o comportamento dinâmico do robô móvel, os valores dos pesos finais são calculados aplicando-se um algoritmo de aprendizado de Hebb. ...
The employment and incorporation of new technologies in the agriculture field allows a new mean- ing to productivity and efficiency. Among its various pillars, autonomous robotics promotes improvements in production, through increased safety in the coexistence between robots and humans, in the execution of various activities. This work presents the use of a low cost prototype controlled by two Fuzzy techniques.The proposed model allows representing the dynamic behaviour of a mobile robot in presence of changes in the environment. A Hierarchical Weighted Fuzzy Logic Controller composes the second navigation system. Simulation results are presented allowing a comparison among both systems and showing the ability of the mobile robot to navigate among obstacles in different scenarios (navigation environment).
... Данные о расстоянии до породы автоматически записываются в файл «Расстояния для остановки.xls» после каждого закрытия этого файла [7,9]. ...
... For instance, geopolitical influence systems are chronologically dependent. Fuzzy time cognitive maps, first approached by [11], included temporary annotations t xy in relations between nodes X → txy Y , denoting a delay t xy before the effect Y is reached. ...
Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed graphs, with nodes denoting causes and links denoting causal influence. A causal graph is a skeletal picture, showing causal associations and impact between entities. Common methods used for graphically representing causal scenarios are neurons, truth tables, causal Bayesian networks, cognitive maps and Petri Nets. Causality is often defined in terms of precedence (the cause precedes the effect), concurrency (often, an effect is provoked simultaneously by two or more causes), circularity (a cause provokes the effect and the effect reinforces the cause) and imprecision (the presence of the cause favors the effect, but not necessarily causes it). We will show that, even though the traditional graphical models are able to represent separately some of the properties aforementioned, they fail trying to illustrate indistinctly all of them. To approach that gap, we will introduce Fuzzy Stochastic Timed Petri Nets as a graphical tool able to represent time, co-occurrence, looping and imprecision in causal flow.
... Fuzzy Grey Cognitive Maps, Intuitionistic Fuzzy Cognitive Maps, and Rough Cognitive Maps are proposed to model uncertain relationships among system components [10]- [12]. Rule-based Fuzzy Cognitive Maps and Extended Fuzzy Cognitive Maps adopt logic rules to express non-linear relationships in FCM [13], [14]. The fuzzy neural networks and wavelet transform are also adopted to improve the performance of the FCM framework in time series forecasting applications [15]- [18]. ...
The Fuzzy Cognitive Map (FCM) is a powerful model for system state prediction and interpretable knowledge representation. Recent years have witnessed the tremendous efforts devoted to enhancing the basic FCM, such as introducing temporal factors, uncertainty or fuzzy rules to improve interpretation, and introducing fuzzy neural networks or Wavelets to improve time series prediction. But how to achieve high-precision yet interpretable prediction in cross-domain real-life applications remains a great challenge. In this paper, we propose a novel FCM extension called Deep FCM for multivariate time series forecasting, in order to take both the advantage of FCM in interpretation and the advantage of deep neural networks in prediction. Specifically, to improve the predictive power, Deep FCM leverages a fully connected neural network to model connections (relationships) among concepts in a system, and a recurrent neural network to model unknown exogenous factors that have influences on system dynamics. Moreover, to foster model interpretability encumbered by the embedded deep structures, a partial derivative-based approach is proposed to measure the connection strengths between concepts in Deep FCM. An Alternate Function Gradient Descent algorithm is then proposed for parameter inference. The effectiveness of Deep FCM is validated over four publicly available datasets with the presence of seven baselines. Deep FCM indeed provides an important clue to building interpretable predictors for real-life applications.
... Some of them stay very true to the basic mechanisms of FCM, while others present a rather different approach. Usually each approach has its own designation (e.g.: DCN -Dynamical Cognitive Networks [28], E-FCM -Extended Fuzzy Cognitive Maps [21], RB-FCM -Rule Based Fuzzy Cognitive Maps [14], etc.); here we use the term Dynamic Cognitive Maps (DCM) to roughly cover such approaches. ...
... However, when used to model the behaviour of qualitative SD traditional FCMs also suffer from a number of drawbacks. These drawbacks largely relate to incomplete: (i) consideration of the semantics of causality [30] and hence the limited capture, representation and simulation of causal dynamics; (ii) inclusion of time relations [31][32][33]; (iii) capture, representation and simulation of fuzziness [34][35][36]; (iv) simulation of dynamics due to the use of single layer perceptron mechanisms [30]. Several extensions of FCMs have been developed to overcome these drawbacks some of the important ones are discussed in the next section, but most of the developed extensions try to solve specific problems with traditional FCMs and do not try to address the issues for modelling the dynamics of complex qualitative systems. ...
Fuzzy Cognitive Maps (FCMs) were developed as a tool for capturing and modelling the behaviour of qualitative system dynamics. However, several drawbacks have been identified that limit FCMs ability in simulating the behaviour of qualitative system. This paper addresses the limitations of FCMs in modelling complex qualitative system dynamics and proposes a generalised Fuzzy Cognitive Mapping (FCM) approach that is able to overcome those limitations. This approach uses fuzzy rules to represent the dynamics of concepts and relations, including time dynamics of relations and introduces a multistep simulation approach that can use several single layer perceptrons to simulate the dynamics of concepts and relations overtime. This approach also incorporates the fuzziness and ambiguity widely associated with expert knowledge when representing and simulating the dynamics of concepts and relations. In this paper, the design of the proposed generalised FCM approach is explained and demonstrated for a real-world case of the consequences of high intensity rainfall in Kampala City, Uganda. This generalised FCM approach creates a new perspective and an alternative approach to model the behaviour of complex qualitative system dynamics using FCMs.
... For the first research point, a number of learning algorithms have been successfully utilized for constructing maps including Hebbian learning, genetic algorithms, memetic algorithms, imperialist competitive algorithms, evolutionary algorithms [10], [16], etc. To satisfy the demand of system modeling regarding complex situations, various extensions of FCMs have been presented one after another from different perspectives including extended FCMs [15], dynamic CMs [17], fuzzy grey cognitive maps (FGCMs) [18], evidential cognitive maps (ECMs) [19], intuitionistic fuzzy cognitive maps (IFCMs) [20], granular cognitive maps (GCMs) [21], interval-valued fuzzy cognitive maps (IVFCMs) [22], extended evidential cognitive maps [24], etc. As pointed out by Pedrycz and Homenda [23], most generalizations which apply information granules to depict the state of concepts and the connection matrix can be regarded as some special cases of GCMs. ...
As a novel generalization of fuzzy cognitive map (FCM), interval-valued fuzzy cognitive map (IVFCM) can provide more flexibility in modeling those increasingly complex system with uncertainty. However, the problem of aggregating IVFCMs has not been considered to this day. Concerning this key point, we propose ensemble IVFCMs via evidential reasoning (ER) approach. Firstly, we give a detailed analysis of IVIFS in terms of evidence theory and introduce the concept of augmented connection matrix within the framework of IVFCMs. Secondly, we present a theory of ensemble IVFCMs using the former work and ER approach, particular emphases are put on assessing the weights of different IVFCMs and aggregating them. Both theoretical analysis and practical examples show that the ensemble IVFCMs not only reflects the importance levels of different maps but also can achieve the goal of merging of information from different maps in system modeling.
... It's noteworthy that the model applied is the same classic from [15] and so, does not consider time, in other words, all concepts take place simultaneously. In this context, there are improvements on FCM that deals with this "disadvantage", for example: E-FCM (Extended-FCM) on [33], RB-FCM (Rule Based-FCM) on [34] and DCN (Dynamic Cognitive Networks) on [35]. There is a recent review of the last 10 years about other improvement applications and training of FCMs. ...
This research aims to develop a Fuzzy Cognitive Map (FCM) and Weighted Classic Fuzzy (WCF) for the satisfaction level of students at Federal Technological University of Parana, Campus Cornélio Procópio (UTFPR-CP). The FCM combines aspects of other intelligent techniques. This tool has inference capacity through concepts and causal relations among them (the influence level among the variables of the model). Its development begins with the determination of the possible areas that would affect or fit as indicators for satisfaction level in UTFPR-CP. Through online forms, it was possible to quantify the influence of the following initially detected areas: professor training, structures of laboratories and classrooms, habitation, library and cleaning. In general, educational institutions do not have tools to provide a critical analysis of its quality. This work proposes a tool for improving the institution in a few years. Thus, with the development of the FCM model, it was possible to identify the positive and negative points that affect the satisfaction level in UTFPR-CP. Finally, to validate the results a WCF was used with same structure and heuristic for comparison with FCM.
... FCMs illustrate the whole system by a graph showing the cause and effect along concepts, and they are a simple way to describe the system's behavior exploiting the accwnulated knowledge of the system (Hagiwara, 1992). The methods that Fuzzy Cognitive Map uses to describe and model the behavior of a system and its application in the modeling the supervisor of large-scale systems have been examined (Stylios, et al., 1998). ...
In Complex Large Scale Systems there is an oncoming need for more autonomous and intelligent systems, new methodologies from discipline research areas have been proposed. A general formulation for the Overall Control Problem of Complex Systems is presented. Then, the use of a hybrid methodology, which combines fuzzy logic and neural networks, Fuzzy Cognitive Map (FCM), for the modeling Supervisory Complex Systems, using is investigated. The description and the construction of Fuzzy Cognitive Map is examined and a model for the supervisor is proposed.
... FCMs have introduced by Kosko (1986Kosko ( ,1992, who enhanced the cognitive maps that had been used in social and political sciences to analyze social decision-making problems; showing a causal relationship between different factors, where the causal relationship is expressed by either positive or negative sign of knowledge expression (Axelrod, 1976). Fuzzy values considered in cognitive maps and FCMs were used to represent causal reasoning (Hagiwara, 1992). Fuzzy Cognitive Maps are used to make decision analysis and cooperate distributing agents (Zhang, et aI. ...
In this paper the application of Fuzzy Cognitive Map (FCM) in controlling a process problem and its use in modelling Supervisory Manufacturing Systems is presented. The description, construction and the mathematical model of Fuzzy Cognitive Map are examined. Then, a chemical process is modelled with FCM and its behaviour is simulated and the application of Fuzzy Cognitive Maps in the mode ling of the Supervisor of Manufacturing Systems is discussed.
... Thus, neuro-fuzzy systems with their ability to incorporate human knowledge and to adapt their knowledge base via new optlmlsation techniques are likely to play increasingly important roles in the conception and design of intelligent control systems (Jang et ai, 1997). FCM is an expert network, which is built by experts, using an interactive procedure of knowledge acquisition (Hagiwara, 1992). ...
The problem of modelling and control of complex systems is addressed. The interrelationship of systems-intelligence and control is analysed and ways to develop Intelligent Control Systems (ICS) are discussed. One useful approach, the Fuzzy Cognitive Maps (FCM), is briefly presented. Issues and challenges that the systems society is confronting with are discussed. Thus researchers and developers who are exploring ways to develop Intelligent Control Systems must give careful attention to the distinctive challenges and unique opportunities of the strong interrelationship and interdependence of the three fundamental fields of science; computers-communications-control.
... o incorporate human knowledge and to adapt their knowledge base via new optimisation techniques are likely to play increasingly impoJ"ta?t roles in the conception and design of hybnd intelligent systems (Jang. et al.. 1997). Fuzzy Cognitive Map is an expert network. which is built by experts. using an interactive procedure of knowledge acquisition (Hagiwara. 1992). ...
The paper examines the usefulness of Fuzzy Cognitive Maps in modeling complex systems and specifically their use in modeling manufacturing systems and information from an abstract point of view. Aspects such as Fuzzy Cognitive Map representation and development are presented and PCM use to develop a behavioral model of the system is discussed. Fuzzy Cognitive Maps applicability in modeling complex systems and their use to aggregate different models for the complex system is discussed. A hierarchical structure is proposed, where a Fuzzy Cognitive Map models the supervisor of the system.
... They have been used to model and simulate many problems that require decision making or classification or prediction/checking of scenarios. Thus, many extensions of the basic FCM model and combinations with other technologies are used in order to better approximate real world problems [6]. Until now, the concept of time has been used in limited cases [7], [8], [9]. ...
... There are also several extensions to classic FCMs that include time in the inference process, for example time discrepancy among concepts in Fuzzy Time Cognitive Maps [9]. Time is also taken into account in Extended FCMs [10], with the introduction of delay nodes between concepts and the use of a Neurocomputing 232 (2017) [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] cause-effect relation function (instead of a cause-effect relation weight factor) in order to deal with systems that do not have constant causeeffect relations. Cause-effect constancy is also dealt with in Rule Based FCMs [11], where relations among concepts are defined with a fuzzy rules base. ...
Fuzzy cognitive maps (FCMs) are distributed computation systems used for qualitative modelling and behaviour simulation. Constructing an FCM is a time-consuming process and the quality of the resulting map is difficult to assess. In this paper we propose an extension to FCMs that self-adjusts the FCM based on real data from the modelled system. The self-adjusting FCM (SAFCM) changes the cause–effect relationships and concept inferences for each system data point with the goal of reducing the error between real data and values produced by the map. In this way, the burden of map construction imposed on the map builder is reduced and the initially constructed map can be evaluated by examining the degree of change caused by the self-adjustment. We tested the SAFCM on two case studies where we measured the degree of change to the initial map structure set up by an expert. The experiments showed that the self-adjusted maps produced results that were closer to real data than the maps that were initially set up by the expert. We also compared the SAFCM to a basic FCM and to an FCM that used a standard learning algorithm. The results showed that our algorithm had higher accuracy.
... Other variations of FCM that are concerned with the "rigid" knowledge representation are known in the literature: E-FCM (Extended-Fuzzy Cognitive Maps) [25], RB-FCM (Rule Based -Fuzzy Cognitive Maps) [26], DCN (Dynamic Cognitive Network) [14], [27], Fuzzy Cognitive Maps with Temporal Granularity [24], Dynamic-Fuzzy Cognitive Maps [1], [28], Rough Cognitive Networks [2], and others. A recent survey with major variations of the classic FCM in recent years that suggests low computational complexity is presented by [29]. ...
... To overcome these drawbacks, the extended fuzzy cognitive maps (E-FCMs) were proposed by Hagiwara [41]. These and other issues led us to explore the questions related to construction of the FCM. ...
... Various extensions of FCMs have been proposed in the literature [28]- [39]. Dynamic cognitive networks (DCNs) appear in [31], and the fuzzy causal networks appear in [32]- [36], while the neutrosophic cognitive maps appear in [37] and [38]. ...
In this chapter, we present a study for the existence of equilibrium points of FCNs equipped with continuous differentiable sigmoid functions that have contractive or at least nonexpansive properties. The study is done by using an appropriately defined contraction mapping theorem and the nonexpansive mapping theorem. It is proved that, when the weight interconnections fulfill certain conditions, related to the size of the FCN and the inclination of the sigmoid functions, the concept values will converge to a unique solution regardless of their initial states, or in some cases a solution exists that may not necessarily be unique.
Otherwise the existence or the uniqueness of equilibria may or may not exist, it may depend on the initial states, but it cannot be assured. In case the FCN has also input nodes (that is nodes that influence but are not influenced by other nodes), the unique equilibrium does not depend solely on the weight set, as in the case of FCNs with no input nodes; it depends also on the values of the input nodes. Numerical examples explore the results and a thorough discussion interprets them.
... Fuzzy cognitive maps (FCMs) are fuzzy-graph structures for representing causal reasoning [7]. FCMs are a visual, formal method used for the symbolic representation of semantic networks and distributed representation of cognitive processes [8]. Applications of FCMs in many fields have appeared, such as precision agriculture [9], software qualify risk analysis [10], diabetes treatment [11], game-based education [12], supervisory control system [13] and structure of Virtual World [14]. ...
The need for effectively developing high quality solutions for very large scale, complex problems continues to drive research in modeling and analyzing System of Systems (SoS). These kinds of systems span numerous domains, including essential infrastructure (water, power, transportation, emergency response, healthcare, education, finance, military, environmental protection etc.). A SoS is composed of independent, autonomous constituent systems; the SoS provides emergent behavior that goes beyond the capabilities of its constituent systems. Having the capability to predict the emergent behavior would be very valuable in assessing the impact of changes in a constituent system's behavior on the emergent behavior of the SoS. For example, if a constituent system is being added, modified, or retired, how will this impact the SoS? In this paper, we explore a new approach to model a SoS, with a focus on emergent behavior for non-functional properties (e.g., safety, reliability etc.,). The approach is based on the visual, formal method Timed-Automata-Based Fuzzy Cognitive Maps (TA-FCMs). A published case study on a water treatment SoS for the Beijing Nanshahe River Basin is used in this work. In future work, we plan to refine our modeling approach and continue on with investigating approach to provide the predictive analysis and formal verification.
As a soft computing method, applying fuzzy cognitive map (FCM) to time series prediction has become a timely issue pursued by numerous researchers. Although many FCM construction methods have emerged, most of them exhibit obvious limitations in weight learning especially for long-term or complex time series. Either the weight calculation is computationally expensive, or it cannot achieve gratifying accuracy. In this paper, a new method for constructing FCM is proposed which extracts concepts from data by exploiting triangular membership function, and the weights of high-order FCM are subtly obtained by transforming the learning problem of FCM into a convex optimization problem with constraints. Since then, FCM with optimized weights is used to represent fuzzy logical relationships of time series and implement prediction further. Fifteen benchmark time series,such as Soybean Price time series, Yahoo stock time series, Condition monitoring of hydraulic systems time series etc. are applied to verify prediction performance of the proposed method. Accordingly, experiment results show that the proposed numerical prediction method of time series is effective and can acquire better prediction accuracy with lower computation time than other recent advanced methods. In addition, the influence of parameters of the method is analyzed individually.
A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an approach allows us to operate in cognitive maps with partially-ordered linguistic variables directly, without vague fuzzification/defuzzification methods. Hence, we may consider more subtle differences in degrees of experts' uncertainty, than in the fuzzy case. We prove the convergence of such cognitive maps and give two simple computational examples which demonstrate using such a partially-ordered uncertainty degree scale compared to the fuzzy case.
Imagery is frequently used to model, represent and communicate knowledge. In particular, graphs are one of the most powerful tools, being able to represent relations between objects. Causal relations are frequently represented by directed graphs, with nodes denoting causes and links denoting causal influence. A causal graph is a skeletal picture, showing causal associations and impact between entities. Common methods used for graphically representing causal scenarios are neurons, truth tables, causal Bayesian networks, cognitive maps and Petri Nets (PNs). Causality is often defined in terms of precedence (the cause precedes the effect), concurrency (often, an effect is provoked simultaneously by two or more causes), circularity (a cause provokes the effect and the effect reinforces the cause) and imprecision (the presence of the cause favors the effect, but not necessarily causes it). We will show that even though the traditional graphical models are able to represent separately some of the properties aforementioned, they fail trying to illustrate indistinctly all of them. To approach that gap, we will introduce Fuzzy Stochastic Timed PNs as a graphical tool able to represent time, co-occurrence, looping and imprecision in causal flow.
Recent years have witnessed the great passion of shoppers to purchase products at promotion, resulting in “smarter” consumers with growing price sensitivity towards promotion. In order to provide such price sensitive consumers with personalized promotion recommendations, it is important to take account of the temporal uncertainty of consumer preference as well as price sensitivity simultaneously. Although consumer preference has been richly studied in recommender system, little attention has been paid to exploring the uncertainty in consumers’ growing price sensitivity. In this regard, this paper seeks to bridge the gap by modeling the temporal dynamics of consumer preference and price sensitivity in a combined manner through the lens of consumer experience evolution. Given the commonly implicit nature of consumer behavior, a pairwise learning framework built on feature-based latent factor model and enhanced Bayesian personalized ranking (exFBPR) is proposed along with a corresponding learning algorithm tailored for experience evolution and multiple feedbacks is developed accordingly. Furthermore, extensive empirical experiments a real-world dataset show the superiority of the proposed framework.
Intuitionistic fuzzy cognitive map (IFCM), an extension of fuzzy cognitive map (FCM), forms a graph-oriented fuzzy model describing both causal relationships among concepts and the states of concepts through intuitionistic fuzzy sets (IFSs). In contrast with FCM, IFCM provides much more flexibility in system modeling. However, IFCMs may lead to confusing or unreasonable results in system modeling, since IFCMs have not fully considered the negative influence from conventional operations on IFSs and the activation process of concepts, and the problem of aggregating knowledge with different importance levels. To overcome the limitations of IFCMs, we propose a high-order IFCM based on evidential reasoning (ER) theory (IFCMR) in this study. Firstly, we introduce an evidential intuitionistic fuzzy aggregation (EIFA) operator and a multiplication operation on IFSs using ER theory. Secondly, we establish the theory of IFCMR based on the EIFA operator and the newly multiplication operation on IFSs. Thirdly, we propose a scheme of aggregating IFCMRs with different importance levels using the EIFA operator, which can also be utilized to aggregate conflict knowledge and to determine objective causal weights in terms of evidential cognitive map (ECM). Finally, a number of numerical examples are utilized to validate the feasibility and validity of IFCMRs in comparison with both IFCMs and ECMs.
Evidential cognitive maps (ECMs) are uncertain graph structure for describing causal reasoning through the cognitive maps (CMs) and Dempster-Shafer (D-S) theory, and utilize the basic probability assignments (BPAs) and intervals to denote connections among concepts and the state of concepts, respectively. ECMs have been proved effective and convenient in modeling those systems with both subjective and objective uncertainty. However, ECMs may get unreasonable results in system modeling when facing the problem of combining knowledge. To overcome the drawbacks of ECMs, we present extended evidential cognitive maps (EECMs) based on evidential reasoning (ER) theory, distance measure and convex optimization for the development of ECMs. In contrast with ECMs, in the EECMs, the default connections are redefined, a scheme of combining knowledge is established through the ER theory, and a convex-optimization-based approach is proposed for determining the weights of different EECMs. Both theoretical analysis and numerical examples indicate that EECMs not only develop ECMs, but also can overcome the limitations suffered by ECMs and other high-order cognitive maps including fuzzy grey cognitive maps (FGCMs), interval-valued fuzzy cognitive maps (IVFCMs) and intuitionistic fuzzy cognitive maps (IFCMs).
Dr. Turksen did not think that his academic career would start with this journey when he was on his way to study Industrial Engineering at the University of Pittsburgh in 1956. The university life that started in 1956 continued for 61 years as both a student and a lecturer and lasted until he retired from the Department of Industrial Engineering at TOBB ETU in 2017. His retirement from the TOBB ETU is his second retirement from the University of Toronto. He earned his bachelor, master and doctoral degrees from the University of Pittsburgh in 1960, 1962 and 1969 respectively. He started teaching at the University of Toronto in 1970 as a lecturer, and his life as an active academician continued until the second half of 2017. He had been teaching and conducting researches including at several universities Toronto, Pittsburgh, METU and TOBB ETU. In addition, he has successfully graduated more than 30 doctoral students and more than 20 graduate students. He formed Knowledge / Intelligence System Lab (KIS) laboratory at the Toronto University and founded IIC Fuzzy Company, where he has signed and finished numerous industry projects. Dr. Turksen's world - wide known career can be seen with all the
details from his resume. Here, I will give a brief assessment of Dr. Turksen's academic knowledge production and the transfer of this knowledge to the industries.
Dr. Turksen has several books published by the world's leading publishing houses, such as Elsevier and Springer. There is a recent book devoted to him covering 50 Year Fuzzy Logic. He also has published more than 40 refereed book chapters. In his own words about the publications he has made in his academic life: "I published more than 170 articles in the journals indexed by (S)SCI and I attended many conferences that I could
not count." When I do a SCOPUS search for Dr. Turksen, the number of publications I get is 266. As you can see, since Dr. Turksen is a scientist with so many publications that can not be referred here, I will make this presentation without giving you a proper reference list. The publications that started in 1963 are still going on today and it will continue in the
coming years.
His Fuzzy Logic researches began with Lotfi Aliasker Zadeh whom he met first during a conference he attended in the mid-1970s. "This is a turning point in terms of my research and understanding of reasoning" he said in his own words. Then his focus turned to the Fuzzy Logic and Fuzzy System Modelling. The main research areas of his study includes (but not limited to); "Fuzzy Logic", "Measuring Fuzziness", "Stochastic Fuzziness", "Decision Systems", "Human-like Reasoning", “Type 1, Interval Valued Type 2 and Type-n Fuzzy Systems", "Fuzzy Hybrid Models". And of course, the application of these models to healthcare, engineering, economics, business and finance. Comparing his research with the history of artificial intelligence reveals parallel development with this field.
Dr. Turksen has worked for more than 40 years developing Full Type 2 Fuzzy Logic, Fuzzy System Modelling, Objective Function Based Fuzzy Systems, Fuzzy Decisions, Hybrid Fuzzy Systems, Fuzzy Clustering Algorithms, and many more topics that I can not list here. He contributed the related literature in a way that many of us willing to do. He also taught and supervised many brilliant minds and has brought many scientists to the
world and Turkey.
I have the honor of being his doctoral student and I feel privileged that I am the friend of one of the most creative, innovative and developing academics in this field; Prof. Burhan Turksen.
This paper examines the usefulness of Fuzzy Cognitive Maps in modeling complex systems and specifically their use in modeling supervisory manufacturing systems and handling with information from an abstract point of view. The use of Fuzzy Cognitive Maps for developing behavioral model for a complex system is discussed. Fuzzy Cognitive Maps applicability in modeling complex systems is presented and a hierarchical structure is proposed to model and control a complex system. Complex system is decomposed in subsystems and for each one a FCM model is developed. A hierarchical structure is proposed where Fuzzy Cognitive Map models the supervisor of the system and develops an abstract conceptual model of the complex system.
The when question of systemic thinking attempts to determine the appropriate time for interacting with our mess
in an effort to increase our understanding about it. Recalling the TAO of systemic thinking
, we must think before we act on (and observe) our mess. The understanding gained from our thinking informs when (and if) we decide to intervene in our mess. In order to discern the appropriate time for action, we explore two criteria of our messes, its
maturity
and its
stability
. These two criteria will first be explored by investigating life cycles and their relevance to the maturity of our mess
. We will then explore the phenomena of evolution
, as it pertains to both biological systems and to purposeful systems. Then, we will discuss entropy as it relates to evolution. Finally, we develop a framework to address the when as it applies to any efforts at intervention in our mess.
Fuzzy Cognitive Maps (FCMs) have been proposed to represent causal reasoning by numeric processing. FCMs have the following features:
(1) They store domain knowledge in nodes and directional connections.
(2) They graphically represent uncertain causal reasoning.
(3) Their matrix representations allow causal inferences to be made as feedback associative memory recollections.
Many researchers have studied FCMs and applied them to various fields. However, there are some shortcomings concerned with knowledge representation in the conventional FCMs. In this paper, we propose Extended Fuzzy Cognitive Maps (E-FCMs) to represent causal relationships more naturally. The features of the E-FCMs are the following:
(1) They can deal with nonlinear causal relationships.
(2) They have time delay weights.
(3) They have conditional weights.
Computer simulation results indicate the effectiveness of the E-FCMs.
The new computing paradigm known as cognitive computing attempts to imitate the human capabilities of learning, problem solving, and considering things in context. To do so, an application (a cognitive system) must learn from its environment (e.g., by interacting with various interfaces). These interfaces can run the gamut from sensors to humans to databases. Accessing data through such interfaces allows the system to conduct cognitive tasks that can support humans in decision-making or problem-solving processes. Cognitive systems can be integrated into various domains (e.g., medicine or insurance). For example, a cognitive system in cities can collect data, can learn from various data sources and can then attempt to connect these sources to provide real time optimizations of subsystems within the city (e.g., the transportation system). In this study, we provide a methodology for integrating a cognitive system that allows data to be verbalized, making the causalities and hypotheses generated from the cognitive system more understandable to humans. We abstract a city subsystem—passenger flow for a taxi company—by applying fuzzy cognitive maps (FCMs). FCMs can be used as a mathematical tool for modeling complex systems built by directed graphs with concepts (e.g., policies, events, and/or domains) as nodes and causalities as edges. As a verbalization technique we introduce the restriction-centered theory of reasoning (RCT). RCT addresses the imprecision inherent in language by introducing restrictions. Using this underlying combinatorial design, our approach can handle large data sets from complex systems and make the output understandable to humans.
Fuzzy Cognitive Networks (FCN) stem from Fuzzy Cognitive Maps (FCM), initially introduced by Kosko to model complex behavioral systems in various scientific areas. This chapter presents basic definitions related to FCM and the traditional way of their operation. It starts with a brief bibliographical introduction, presenting various extensions of the initial model and areas of application. Since their convergence is a crucial point for the development of Fuzzy Cognitive Networks, particular emphasis is given to the subject of their convergence to equilibrium points and some noticeable peculiarities that may appear. Then, the scope of Part II of this book is analyzed and the organization of the relevant chapters is presented.
The Fuzzy Cognitive Map (FCM) has emerged as a convenient and powerful soft modeling tool since its proposal. During the last nearly 30 years, Fuzzy Cognitive Maps have gained considerable research interests and have been applied to many areas. The advantageous modeling characteristics of FCMs encourage us to investigate the FCM structure, attempting to broaden the FCM functionality and applicability in real world. In this paper, the main representation and inference characteristics of conventional Fuzzy Cognitive Maps are investigated, and also the current state of the extensions of FCMs, learning algorithms for FCMs is introduced and summarized briefly.
The increase in the number of security breaches has made information security risk management an essential security activity for all type of organizations. Risk Management involves assessment involves identification of assets, threats and vulnerabilities. Attacks by outsiders continue to cause the most security breaches to all organizations. Existing approaches like attack graph based risk assessment have scalability issues and focus on only single step attacks. It is very difficult to predict multistep attacks that exploit a chain of vulnerabilities. The multistep attacks are based on the causality of relation where every cause has an effect. Causality refers to a cause i.e. one event and consequences i.e. another event that has occurred because of the cause. The proposed system aims to make use of fuzzy cognitive maps to model the causally dependent events. Fuzzy cognitive map is a concrete representation of knowledge that can handle incomplete or conflicting information. This is very important in risk assessment because important information may be unreliable as they may be a result of unreliable measurement techniques. The proposed system will aid in proactive information security risk assessment.
Time is a basic aspect in any field, as factors evolve over time and influence the progression of any procedure. This work proposes an integrated approach to developing Timed Fuzzy Cognitive Maps (T-FCMs), an extension of FCMs that can handle uncertainty to infer a result. TFCMs take into consideration the time evolution of any procedure and permit the production of intermediate results and the influence of exterior parameters. It described the proposed method to develop T-FCM and then T-FCM is applied to develop a Medical Decision Support System.
The authors present a time-delay neural network (TDNN) approach to
phoneme recognition which is characterized by two important properties:
(1) using a three-layer arrangement of simple computing units, a
hierarchy can be constructed that allows for the formation of arbitrary
nonlinear decision surfaces, which the TDNN learns automatically using
error backpropagation; and (2) the time-delay arrangement enables the
network to discover acoustic-phonetic features and the temporal
relationships between them independently of position in time and
therefore not blurred by temporal shifts in the input. As a recognition
task, the speaker-dependent recognition of the phonemes B, D, and G in
varying phonetic contexts was chosen. For comparison, several discrete
hidden Markov models (HMM) were trained to perform the same task.
Performance evaluation over 1946 testing tokens from three speakers
showed that the TDNN achieves a recognition rate of 98.5% correct while
the rate obtained by the best of the HMMs was only 93.7%
A neural network learning procedure has been applied to the classification of sonar returns from two undersea targets, a metal cylinder and a similarly shaped rock. Networks with an intermediate layer of hidden processing units achieved a classification accuracy as high as 100% on a training set of 104 returns. These networks correctly classified up to 90.4% of 104 test returns not contained in the training set. This performance was better than that of a nearest neighbor classifier, which was 82.7%, and was close to that of an optimal Bayes classifier. Specific signal features extracted by hidden units in a trained network were identified and related to coding schemes in the pattern of connection strengths between the input and the hidden units. Network performance and classification strategy was comparable to that of trained human listeners.
Using a compound-valued logic, a logical architecture is introduced for representing fuzzy cognitive maps and for modeling knowledge acquisition in adaptive bidirectional associative memories. The excitatory, neutral, and inhibitory values of causal relations provide an effective paradigm for knowledge acquisition and processing. The main contribution is a NPN (negative-positive-neutral) calculus that is used as a logical inference engine.< >
A contribution to the theoretical development of fuzzy neural
network theory is presented. Three types of fuzzy neuron models are
proposed. Neuron I is described by logical equations of `if-then' rules;
its inputs are either fuzzy sets or crisp values. Neuron II, with
numerical inputs, and neuron III, with fuzzy inputs, are considered to
be simple extensions of non-fuzzy neurons. A few methods of how these
neurons change themselves during learning to improve their performance
are also given. The application of the non-fuzzy neural network approach
to fuzzy information processing is briefly discussed
Estimation of expert weights using fuzzy cognitive maps
- W R Taber
- M A Siegel