Broumi Said

Université Hassan II de Casablanca

In The traveling salesman problem (TSP) is an essential and the most popular conventional combinatorial optimization network problem in operations research, in which the TSP evaluates the shortest route or path in a network. In TSP, every node has been visited only once, excluding the starting node. In TSP, edge lengths are usually expressed to ind...

Fuzzy sets have long been employed to handle imprecise and uncertain information in the real world, but their limitations in dealing with incomplete and inconsistent data led to the emergence of neutrosophic sets. In this thought-provoking book, titled Data-Driven Modelling with Fuzzy Sets: A Neutrosophic Perspective, the authors delve into the the...

The primary purpose of this report is to present an idea that is considered one of the main ideas in neutrosophic binary topological spaces. We plead them the axioms of neutrosophic binary separation axioms associated in the neutrosophic binary kernel. Also we studied its characteristics and the relationships between these new neutrosophic binary s...

The primary purpose of this report is to present an idea that is considered one of the main ideas in neutrosophic binary topological spaces. We plead them the axioms of neutrosophic binary separation axioms associated in the neutrosophic binary kernel. Also we studied its characteristics and the relationships between these new neutrosophic binary s...

All rights reserved. The authors of the articles do hereby grant Neutrosophic Systems with Applications a nonexclusive, worldwide, royalty-free license to publish and distribute the articles in accordance with the Budapest Open Initiative: this means that electronic copying, distribution, and printing of both full-size versions of the journal and t...

Jaikumar, R. V., Sundareswaran, R., Broumi, S., & Al-Hawary, T. A. (2024). Vulnerability parameters in picture fuzzy soft graphs and their applications to locate a diagnosis center in cities. Journal of fuzzy extension and applications, 5(1), 86-99. Abstract The notion of Fuzzy Graphs (FGs) and Intuitionistic Fuzzy Graphs (IFGs) is generalized in t...

The Neutrosophic Bonferroni operator is a novel operator that we provide in this paper. Then the arithmetic operations for Neutrosophic Bonferroni operator is developed which tells the existence of Neutrosophic Bonferroni operator. Then its properties were discussed with special cases. To group decision-making issues with several attributes, arithm...

Chapter 8: Quota Harvesting Logistic Growth Model: A Neutrosophic Differential Equation Approach

Neutrosophic sets play a crucial role in handling uncertainty, ambiguity, and indeterminacy in numerous theories. They are a kind of extension of the two types of fuzzy sets and intuitionistic fuzzy sets. In the context of modeling drug diffusion within human connective tissues, a differential equation is employed within the neutrosophic framework,...

The goal of this article is to establish a methodology for ordering of single-valued neutrosophic numbers (SVN-numbers) on the basis of values and ambiguities. First of all, the idea of neutrosophic numbers is discussed, and (α, β, γ)-cut and arithmetic oprations definecd over SVN-numbers are examined. Thereafter ,corresponding to each components,t...

This paper recommends and designs concepts for evaluating the shortest path (SP) for a connected network using a modified breadth-first search algorithm in an uncertain environment. Evaluating the SPs of a network is an essential and extensively encountered optimization problem. Here we develop a new method for determining the SP in a neutrosophic...

Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inco...

Over the past few years, we have seen the spread of wireless networks in institutions, businesses, and private homes. Their wide variety, market availability, and ease of implementation have made this wireless technology more popular than wired networks. Nevertheless, enterprises are still demanding better quality of service to meet the needs of se...

In this paper, a maple code is presented to do many operations on interval valued neutrosophic matrices including entering the elements of the matrix, checking whether a given matrix is an interval valued neutrosophic matrix or not, finding complement of an interval valued neutrosophic matrix, finding score, accuracy, and certainty measures, union...

This is Volume 59 of Neutrosophic Sets and Systems, a special issue about symbolic n-plithogenic algebraic structures and their applications

Contemporary mathematical techniques have been crafted to address the uncertainty of numerous real-world settings, including Fermatean neutrosophic fuzzy set theory. Fermatean neutrosophic fuzzy set is an extension of combining Fermatean and neutrosophic sets. Fermatean neutrosophic set was developed to enable the analytical management of ambiguous...

In this paper, we redefine the dense neutrosophic set operations and, by using them, we introduce new definition for D − topological space in neutrosophic topological space and also gives the basic specifications for the new definitions of neutrosophic D − topological space in neutrosophic topological space, we also obtained some properties that sh...

The Neutrosophic Set (𝑁𝑠𝑒𝑡) represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true (𝓣𝒓), false (𝓕𝒂), and indeterminacy 𝓘𝒏 values crosses the membership value of one, that is, 𝓣𝒓 + 𝓘𝒏 + 𝓕𝒂 < 1. It becomes more crucial during decision-making processes like med...

In this paper, we present the Pythagorean neutrosophic interval valued fuzzy soft set. This is a generalization of the Pythagorean interval valued fuzzy soft set as well as the neutrosophic interval valued fuzzy soft set. It is discussed in this paper how an aggregated operation is used to aggregate the decision matrix of PNIVS. There are a number...

In contrast to the Pythagorean interval valued fuzzy soft set and the neutrosophic interval valued fuzzy soft set, the Pythagorean neutrosophic interval valued fuzzy soft set is a generalization of these sets. We discuss aggregating PyNIVFS decision matrixes by using aggregated operations. The VIKOR method, which is an extension of neutrosophic fuz...

In this study, a Neutrosophic technique and arithmetic ranking operations are employed to group decision-making problems with many qualities. The outcome is contrasted with the current approach. When compared to the current method, the proposed method is much more manageable and useful for solving group decision making problems involving several qu...

Multicriteria group decision-making scenarios with a large number of criteria values may be challenging for experts to control. This is a result of the specialists' need to consider an excessive amount of data. They find it difficult to make the optimal decision since the possibilities overwhelm them. We propose a novel multicriteria group decision...

Graph theory is a developing field which has many advancements and developments in real-life applications. Although graph theory has rapid growth in modeling real-life issues, some vague details in real-life problems are hard to picture using the usual graph. Fuzzy graph theory is known for its applications in modeling the human thinking, which has...

Industry 5.0 acceptance is accelerating, but research is still in its infancy, and existing research covers a small subset of context-specific obstacles. This study aims to enumerate all potential obstacles, quantitatively rank them, and assess interdependencies at the organizational level for Industry 5.0 adoption. To achieve this, we thoroughly r...

In this research, we are examining a study that enables us to generate Neutrosophical random variables that follow probability distributions based on Neutrosophical random numbers that follow for the uniform distribution, using the rejection and acceptance method, which depends on the largest value taken by the probability density function of the d...

A key aspect of human cognition is learning, a universal process that all humans undergo. In order to learn or improve one's knowledge and abilities, it integrates influences from the cognitive, emotional, and environmental spheres. There are vast amounts of studies and a wide range of hypotheses that attempt to describe the workings of the learnin...

Correlation is a statistical measure that expresses the extent to which two variables are linearly related. It's a common tool for describing simple relationships without making a statement about cause and effects. Correlations are useful for describing relationships among data. In this chapter, the authors are applying the correlation coefficient...

The education system of a country to its citizens determines its success. The primary goal of providing education is to mold a person's entire personality and shape his career. Everyone, regardless of caste, creed, religion, gender, or any other factor, must have access to their choice's high-quality and indiscriminate education. At present, povert...

In the community of generalized fuzzy sets, the notion of single-valued neutrosophic sets (SVNSs) enables individuals to express their preferences by processing the indeterminate information, thus it plays a significant role in intelligent information processing. For addressing teamwork assessment tasks in the education setting, this chapter concen...

One of the components of the educational teaching process is evaluation. The teacher evaluates the students at different moments of the course, to control that they adequately comply with the general and specific objectives that are proposed in the curriculum. This chapter describes a software called “Students' Skills Evaluator 1.0,” designed by th...

The field of education is witnessing paradigm changes, especially with reference to characterization of teachers and their roles. The inception of digital learning portals has widened the information sources of the learners and masked the belief of teachers as the only pool of knowledge. The mutating pedagogies have defined teacher as a facilitator...

The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, as it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \us...

Let N = (V, E) be a simple graph and let X be a subset of V (N). If every node not in X lies on a geodesic path between two nodes from X then it is called a geodetic set. The geodetic number g (N) is the minimum cardinality of such set X. The subset X is called a dominating set if every node not in X has at least one neighbour in X. The minimum num...

This paper provided new concepts of neutrosophic crisp continuous functions named neutrosophic crisp αg-continuous, neutrosophic crisp gα-continuous, neutrosophic crisp gαg-continuous, neutrosophic crisp gαg*-continuous and neutrosophic crisp gαg**-continuous functions and their relations.

Face-on-Face interaction constitutes an integral part of the classroom atmosphere as it provides teachers with an opportunity to understand their students intimately. Hence, this study deals with attribute based double bounded rough neutrosophic set driven random forests using Gini Impurity based split to arrive at a decision regarding the teaching...

It is well known that the unpredictable speech production brought on by stress from the task at hand has a significant negative impact on the performance of speech processing algorithms. Speech therapy benefits from being able to detect stress in speech. Speech processing performance suffers noticeably when perceptually produced stress causes varia...

Security system is the process of developing, adding, and testing security features within applications to prevent security vulnerabilities against threats such as unauthorized access and modification. The implementation of such secure message passing protocols and the best, most dependable computing algorithms are made possible by hyperideal archi...

In this paper we have successfully constructed the literal neutrosophic Kumaraswamy probability distribution. We mean by literal neutrosophic probability distribution that parameters of the distribution and the values that the random variable describing the distribution all take literal neutrosophic numbers of the form = + ; 2 = which differs from...

Business firms prefer software-based smart manufacturing systems to monitor and supervise all production activities in a decentralized manner. The choice of software decides the degree of manufacturing robustness. This paper proposes a neutrosophic-based MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) method of MCD...

In this paper, we delivered pioneering notions of closed sets in the neutrosophic crisp sense. In other words, we discussed sg-closed sets, gs-closed sets, and gsg-closed sets in neutrosophic crisp topological space. Moreover, the subsequent innovative ideas are established, for instance, gsg-closure and gsg-interior in neutrosophic crisp topologic...

In this article, we presented a ranking system based on the sign distance in a new direction, such that to compare different single-valued neutrosophic numbers (SVN-numbers), a decision maker has the chance of flexibility. We also developed some important definitions, like level-(α,β,γ) neutrosophic point, and some properties related to the sign di...

Graph theory is a developing field which has many advancements and developments in real-life applications. Although graph theory has rapid growth in modeling real life issues, some vague details in real-life problems are hard to picture using the usual graph. Fuzzy graph theory is known for its applications in modeling the human thinking, which has...

Vagueness and uncertainty are two distinct models are represented by Fuzzy sets and Soft sets. The combination of Soft sets and simple graphs produces soft graphs which is also an interesting concept to deal with uncertainty problems. Any communication network can be modelled as a graph whose nodes are the processors (stations) and a communication...

The interval-valued quadripartitioned neutrosophic set is represented by the partition of the interval-valued neutrosophic set’s indeterminacy function into contradiction and ignorance parts. This article introduces the properties of interval quadripartitioned single valued neutrosophic graph. The properties like complementary, self-complementary,...

During the production process, production companies need to monitor the finished products and ensure their quality, which imposes on them the appointment of inspectors for auditing, and this appointment costs the company amounts that affect the general profit, so it strives to make this cost as low as possible and that the audit process is carried...

The directed rough fuzzy graph (DRFG) is a fusion of rough and fuzzy theory, because it deals with incomplete and vague information simultaneously. Connection or the strength of connectivity (SC) is vital in the realm of circuits or networks that are linked to the real world. As a result, SC is one of the most essential aspects of a directed rough...

The following paper introduces a methodology to calculate the least cost for a directed network through the Travelling salesman problem. The dynamic programming method is used to find the minimum cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic sets...

Medical images are essential in contemporary medicine because they provide practicable entropy, which is used to diagnose medical conditions. It is useful to visualize abnormality in several parts of the body. Image segmentation in the medical has an important function in various applications in diagnosis systems. Researchers have become interested...

This research article represents an innovative concept in Plithogenic Combined Disjoint Block Fuzzy Cognitive Maps (PCDBFCM) and its applications. PCDBFCM is a very useful tool in grouping the factors with contradiction degree of multiple attributes. A plithogenic fuzzy matrix is used to represent the connection matrix. The resultant vector is obta...

The Neutrosophic number is defined to solve the vagueness of the real-life problem and to analysis the indeterminacy of the problem, the paper defines a special single valued Decagonal Neutrosophic number and De-Neutrosophication formula are formulated using the removal area method and a numerical practical example is illustrated of network path ed...

Indeed, one of the most well-known topics in the area of graph theory is the shortest path (SP) problem, which has practical applications in various areas of research, including transportation, communication via networks, life-saving services, fire department services, etc. The edges of the connected SP problems are typically characterized by vario...

In general, companies are investing a lot of energy and time in conserving the quality of the products. The customers use the attribute of quality as the measuring index of the efficiency of these companies. Quality sustenance is not a phase, but it is a process which must be carried out till the product reaches the end consumer. This is possible b...

This article employs the conception of neutrosophic generalized -closed sets to construct a further weakly class of neutrosophic contra continuous mappings for instance neutrosophic contra generalized -continuous mappings via neutrosophic topological spaces. Additionally, essential related attributes and various theorems and related features and no...

In this study, we presented a new generalization of the Fermatean interval valued fuzzy soft set (FIVFSS) and the neutrosophic interval valued soft set called the neutrsophic Fermatean interval valued soft set (NSFIVSS). The NSFIVSS decision matrix aggregated operations are the topic of our current discussion. Strong points of view for the generali...

We discuss innovative square root Diophantine neutrosophic normal interval-valued set (SRDioNSNIVS)-based approaches to multiple attribute decision-making (MADM) problems. Square root neutrosophic sets, interval-valued Diophantine neutrosophic sets and neutrosophic normal interval-valued (NSNIV) sets are both extensions of square root Diophantine n...

In this work, we define Interval-valued Fermatean neutrosophic graphs and present some operations on Interval-valued Fermatean neutrosophic graphs. Further, we introduce the concepts of Regular interval-valued Fermatean neutrosophic graphs, Strong interval-valued Fermatean neutrosophic graphs, Cartesian, Composition, Lexicographic product of interv...

The quadripartitioned neutrosophic set is the partition of indeterminacy function of the neutrosophic set into contradiction part and ignorance part. In this work, the concept of quadripartitioned neutrosophic graph structures and its properties are invented. The strong, tree, 𝜙 − permutation and 𝜙 − complement of quadripartitioned neutrosophic gra...

Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features are examined as wel...

Collected Papers on Neutrosophics and other topics

Road traffic management has been a serious concern in the transportation sector for many years now. The explosion in the number of cars along with the inability of creating new highcapacity road infrastructures in big cities makes mitigating this danger a problem for the scientific research community. Traffic congestion contributes to increased pol...

This paper introduces the generalized q-rung neutrosophic soft set (GqRNSSS) theory and its use to solve actual problems. We also define a few operations that make use of the GqRNSSS. The GqRNSSS is constructed by generalizing both the Pythagorean neutrosophic soft set (PyNSSS) and Pythagorean fuzzy soft set (PyFSS). We give a method for agricultur...

This study reveals new concepts of neutrosophic crisp closed sets named neutrosophic crisp g-closed sets, neutrosophic crisp ag-closed sets, neutrosophic crisp ga-closed sets, and neutrosophic crisp gag-closed sets. Furthermore, their ultimate features in neutrosophic crisp topological spaces are examined. Moreover, the consequent new concepts are...

The paper provided a new notion of neutrosophic separation axioms as neutrosophic gag-Ri-space & neutrosophic gag-Tj-space (note that the indexes i & j are natural numbers of the spaces R & T are from 0 to 1 & from 0 to 2 alternately). Mathematical Subject Classification (2010): 54A40.

This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophic Theories and their Applications, published between 2013-2021 in the international book series about neutrosophic sets and systems by the author alone or in collaboration with the following 112 co-authors (alphabetically ordered) from 21 countries: Abdel...

In this paper, we intend to utilize the ideas of Neuα-open and Neusα-open sets to distinguish several novel conceptions of weakly neutrosophic continuous functions, for instance; -continuous, Neuα**-continuous , Neusα-continuous, Neusα*-continuous and Neusα**-continuous functions. Moreover, we will describe the interactions among these thoughts of...

Purpose This research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels. Design/methodology/approach Due to the lack of reliable information, changeable economic circumstances, uncontrolled factors and esp...

Neutrosophic set (NS) is generalization of Intuitionistic Fuzzy Set(IFS) and Fuzzy Set (FS) where Neutrosophic Set(NS) is the collection of Membership, Non-Membership, Indeterminacy Membership of the constituent element. This paper includes the modified circle breaking techinque which is used to evaluate the Shortest Path Problem in which edge weig...

Let X be a finite set having n elements. The formula for giving the number of topologies T(n) is still not ob�tained. If the number of elements n of a finite set is small, we can compute it by hand. However, the difficulty of finding the number of the topology increases when n becomes large. A topology describes how elements of a set are spatially...

This study included concepts for (, ε, ς)-single valued neutrosophic hyperring ((, ε, ς)-SV N HR) and (, ε, ς)-single valued neutrosophic hyperideal ((, ε, ς)-SV N HI). (, ε, ς)-single valued neutrosophic hyperrings ((, ε, ς)-SV N HRs) and (, ε, ς)-single valued hyperideals ((, ε, ς)-SV N HIs) are examined and validated in terms of algebraic featur...

In this paper, we introduce the concept of balanced neutrosophic graphs based on density functions and investigate some of their properties. The necessary conditions for a neutrosophic graph to be a balanced neutrosophic graph are identified if graph G is a selfcomplementary, regular, complete, and strong neutrosophic graph. Some properties of comp...

Recently, the intelligent traffic control system and its uncertainty analysis are considered one of the hot spots for utilizing the available techniques. It became more essential when the automatic car, electric vehicle, and other smart cars have introduced the transportation. To control the traffic accident and smooth road services an intelligent...

Fuzzy soft graphs are effective mathematical tools that are used to model the vagueness of the real world. A fuzzy soft graph is a fusion of the fuzzy soft set and the graph model and is widely used across different fields. In this current research, the concept of picture fuzzy soft graphs is presented by combining the theory of picture soft sets w...

The objective of any decision-making method in a plithogenic environment is to make an optimal ranking of the alternatives subjected to core essential criteria. The preference for plithogenic decision-making methods is gaining momentum in recent times as plithogenic representations are more comprehensive and efficient in handling uncertain and impr...

Traffic congestion is a great concern, especially in urban areas where the vehicles’ number on roads continues to intensify significantly against the slow development of road infrastructure. To resolve this intractable problem, researchers proposed various Traffic Management Systems that rely on the fusion of traffic data sources and emerging techn...

The article considers a new generalization of closed sets in neutrosophic topological space. This generalization is called neutrosophic ℊsℊ-closed set. Moreover, we discuss its essential features in neutrosophic topological spaces. Furthermore, we extend the research by displaying new related definitions such as neutrosophic ℊsℊ-closure and neutros...

The advance payment of acquiring cost is mostly encouraged by both supplier and retailer in current situations. This chapter discusses the economic order quantity model with multiple payments of acquiring cost in advance at equal intervals. The current research examines two-warehouse economic order quantity model with imperfect items under neutroso...

The investigation of a person’s symptoms can be evaluated through medical diagnosis to diagnose the diseases. To medical clinicians, a large amount of data is available for diagnosis, which comprises uncertainty, inconsistency, and indeterminacy. The field of medicine is one of the best areas of application for neutrosophic set theory. The main int...

In this paper, we present a maple programming code that helps useres and scientific researchers to input single valued neutrosophic matrices, checks whether inputted matrix is single valued neutrosohic matrix, finds the complement of a single valued neutrosophic matrix, calculates score matrix, accuracy matrix and certainty matrix, finds the union...

Collected Papers (on Neutrosophic Theory and Applications) Volume VI

The current study shows the study of NeutroBitopological Space. In this work, the properties of NeutroBitopological Space are discussed. It is seen that many properties do not coincide with the properties of general Bitopological space. The terms NeutroInterior, NeutroClosure, and NeutroBoundary are defined with examples also their properties ar...

Let = (U, V) be a Single valued Neutrosophic graph. A subset ∈ () is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, | ()-()| ≤ 1, , ∊. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S...

Let = (U, V) be a Single valued Neutrosophic graph. A subset ∈ () is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, | ()-()| ≤ 1, , ∊. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V − S...

In this paper is to introduce trapezoidal neutrosophic deal with logarithmic demand model with shortage of deteriorating items. Order of enact customers can be place by the vendor depending on the stock accessibility. Logarithmic demand is related to several products, in this paper developed with the shortage of items at the beginning. Finally, val...

This paper is to introduce a two-warehouse system for trapezoidal bipolar neutrosophic disparate expeditious worsen items with power demand pattern is dealt. Inventory worsens in the both storehouses disparate fixed amount. Demand is considered three different models (a) increasing demand (b) decreasing demand (c) linear demand. The model effective...

A hybrid assessment method of a group’s overall performance with respect to a certain activity is developed in this paper using soft and neutrosophic sets as tools and it is applied for student assessment. The present method is compared with another method developed in an earlier authors’ work, which uses soft sets and grey numbers as tools for the...