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The article presents new types of fuzzy sets, such as the hypersoft set, indeterminate soft set, indeterminate hypersoft set, and tree soft set. Definitions and examples of these sets are provided, as well as practical applications. Other fuzzy extensions of the soft set are also mentioned, and the possibility of investigating and applying new forms of soft sets in combination with fuzzy sets and their extensions is suggested. The author of the article is Florentin Smarandache from the University of New Mexico. The text was published in the Octogon Mathematical Magazine and Journal of Fuzzy Extension and Applications. [Extracted from the article]

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a novel methodology to the three-way decision idea. Initially, we revamp the three-way decision model using rough set theory and incorporate interval-valued classes to handle intuitionistic fuzzy data. Secondly, we explore the use of intuitionistic fuzzy power weighted and intuitionistic fuzzy power weighted geometric aggregation operators to consolidate attribute values within the data system. Furthermore, we present a case study in the medical field to exhibit the validity and efficiency of our offered technique. This innovative method enables us to classify participants into three distinct zones based on their symptoms. The manuscript concludes with a summary of key points provided by the authors. [ABSTRACT FROM AUTHOR]

The concept of q-rung orthopair neutrosophic set is introduced in this paper and fundamental properties of it are studied. Also the ordinary notion of topological space is extended to q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness and Hausdorff topological space. All these generalizations are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q -rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative's dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. [ABSTRACT FROM AUTHOR]

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That's why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements' degrees of truth/indeterminacy/falsehood are evaluated by many (Multi) sources. Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets. Several particular cases of the MultiNeutrosophic Sets are presented: such as MultiFuzzy Set, MultiIntuitionistic Fuzzy Set, MultiPicture Fuzzy Set, and other Multi(Fuzzy Extension) Set. [ABSTRACT FROM AUTHOR]

Plithogenic sets coined by Smarandache in the year 2018 has unveiled new research opportunities in the field of Multi criteria decision making (MCDM). The contributions and developments of new decision making approaches based on plithogeny is gaining high momentum presently. The theoretical conceptualization of different phenomenon with plithogenic sets are also applied in designing optimal solutions to the decision making problems. This review paper presents the applications of plithogenic MCDM from the year 2018 to till date in almost all the spheres of decision making scenario. The literature works of the researchers presented in this paper will certainly portray the compatibility and flexibility of plithogenic sets, operators and other decision making tools. Though the time span considered for counting on the plithogeny based works is short, the applications of plithogenic sets are growing many in number and also plithogeny based theories are amplifying in a speedy manner. This has motivated the authors to investigate on the proliferation of plithogeny applications in decision making. This review paper has focused on the dimensions of different fields to which plithogeny is applied, new plithogeny based theories, extension of plithogeny, plithogenic based operators and measures. In addition to it the data on the publications of plithogeny based articles and interests of researchers are also presented as a part of this review work. The overall impact of plithogeny in the arena of decision making science and on the researchers of the same field is well sketched in this paper with the intention and hope of inspiring plithogenic researchers. [ABSTRACT FROM AUTHOR]

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here. [ABSTRACT FROM AUTHOR]

Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model. [ABSTRACT FROM AUTHOR]

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented them as Plithogenic Attributive Subjectively Whole Hyper-Super-Soft-Matrix (PASWHSS-Matrix) and Plithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. [ABSTRACT FROM AUTHOR]

This paper is devoted to plithogeny, plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems. [ABSTRACT FROM AUTHOR]

This work is the continuation of our recent work entitled n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS). In this paper, we present n-Cylindrical Fuzzy Neutrosophic (n-CyFN) continuous functions and related results. A characterization on n-CyFN continuous functions is proposed as well. Along with familiarising the n-CyFN interior and n-CyFN closure of sets in n-Cylindrical Fuzzy Neutrosophic Topology (n-CyFNT) and its basic theorems, we define n-CyFN open function, n-CyFN closed function and n-CyFN homeomorphism. [ABSTRACT FROM AUTHOR]

When compared to its extension, hypersoft set, a soft set only deals with a single set of attributes, while a hypersoft set deals with several attribute-valued disjoint sets that correspond to various attributes. Several researchers have developed models based on soft sets, but the majority of these models suffer from limitations since they are inappropriate for interval-type data or uncertain data. In order to address these issues, a novel model interval-valued fuzzy hypersoft set (IV FHS-set) is presented in this research article. This model not only resolves the inadequacy of soft set for distinct attributes for non-overlapping attribute-valued sets, but also addresses the limitations of soft set-like models with having data in interval environment. This work modifies the current fuzzy hypersoft set concept and introduces certain fundamental ideas, such as subset, not set, whole set, and absolute relative null set, relative absolute set and aggregation operations e.g. intersection, union, extended intersection, restricted union, complement, OR, AND, difference, restricted difference are discussed under IV FHS-set environment with illustrated examples. Some new hybrids of fuzzy hypersoft set under interval-valued settings are also discussed. Moreover, some extensions of IV FHS-set are presented along with different operations. [ABSTRACT FROM AUTHOR]

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets. [ABSTRACT FROM AUTHOR]

In this paper, Neutrosophic definitions and properties of some special number sequences which are frequently found in the science literature, called Neutrosophic Number Sequences (NNSq) via Horadam sequence are studied for the first time. Especially for Neutrosophic Fibonacci (NFNq) and Neutrosophic Lucas (NLNq) number sequences, fundamental properties and identities such as Ruggles, Honsberger, Cassini, Catalan, d'Ocagne, and Tagiuri are given. In addition, Neutrosophic definitions of the sequences of Pell (NPNq), Pell-Lucas (NPLNq), Jacobsthal (NJNq), Jacobsthal-Lucas (NJLNq), Mersenne (NMNq), Mersenne-Lucas (NMLNq), Balancing (NBNq), and Lucas-Balancing (NLBNq) numbers are introduced. Besides defining these numbers and their sequences, since fuzzy and intuitionistic fuzzy sets are restrictions of neutrosophic sets, sequences of numbers within these sets are naturally and indirectly revealed. [ABSTRACT FROM AUTHOR]

COVID-19 outbreak is a reminder of the fact that the pandemics have happened in the past and will also occur in the future. The COVID-19 not only has affected the economy; but also it has affected the livelihood, which leads to the changes in businesses. This study aims to identify the most significant indicator (or parameter) that impacts the sustainability of industries. The study should also develop a realtime monitoring system for the sustainability of industries affected by COVID 19. In this work, the Polynomial Neural Network (PNN) and cosine similarity measure under SVPNS (Single-Valued Pentapartitioned Neutrosophic Set) environment have found their use in analyzing the sustainability of the industry. [ABSTRACT FROM AUTHOR]

The mathematical operations of convergence, association, supplement, arithmetical total, logarithmic item, scalar increase, and exponentiation are the main topics of this article. We show certain important logarithmic features of idempotency, commutativity, associativity, retention, distributivity, and De Morgan's laws over the addition of Neutrosophic fuzzy sets. We also outline new fixations and NFS widening and show some concepts in action. Last but not least, we define a further operation (@)on Neutrosophic fuzzy sets and investigate distributive laws for the case where the responsibilities of ⊕, ⊗, ∪, and ∩ are combined. [ABSTRACT FROM AUTHOR]

In this paper we prove that Neutrosophic Statistics is an extension of the Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities, andhas more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some applications, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics that are the most general forms of MultiVariate Probability and MultiVariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). [ABSTRACT FROM AUTHOR]

Aggregation operators can be used to combine and synthesise a finite number of numerical values into a single numerical value. Many areas, including decision-making, expert systems, risk analysis, and image processing, rely heavily on aggregating functions. In real-world situations, the neutrosophic set can manage the uncertainties associated with information from any decision-making challenge, whereas the fuzzy set and intuitionistic set cannot. The term "bipolarity" refers to the propensity of the human mind to weigh pros and drawbacks when thinking through decisions. Triangular norms are aggregation operators in a variety of fields, including fuzzy set theory, probability and statistics, and decision sciences. Thus, the individual assessments in this paper's study of and approach to multi-criteria decision-making (MCDM) problems that use bipolar neutrosophic numbers as the individual evaluations. Frank operational laws of bipolar neutrosophic numbers, bipolar neutrosophic Frank weighted geometric aggregation (BNFWGA) and the bipolar neutrosophic frank ordered weighted geometric aggregation (BNFOWGA) operators have been developed with its desirable properties. Additionally, the suggested aggregation operators have been used in the selection of bridges. The outcomes demonstrate the applicability and validity of the suggested approach. Comparative analysis has been performed using the current approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of fuzzy Neutrosophic set called n-Cylindrical fuzzy Neutrosophic set (n-CyFNS), with I as independent neutrosophic component. The n-CyFNS can be claimed as the largest extension of fuzzy sets. In n-CyFNS, the degree of positive, neutral and negative membership functions are satisfying the condition, 0≤ βA(x) ≤1 and 0≤ αA n(x) + γA n(x) ≤ 1, n>1, is an integer. Also the distance between two n-CyFNS and its properties are also defined. Along with basic operations on n-CyFNSs, we put forward two concepts-Neutrosophic affinity degree & Neutrosophic similarity index which is used to compare and correlate n-CyFNSs respectively. A comparison is made in the n-CyFNS environment using the existing correlation measures to check its reliability. [ABSTRACT FROM AUTHOR]

Fuzzy hypersoft set (FHS-set) is an effective and flexible model as it not only minimizes the complexities of fuzzy set for dealing uncertainties, but also fulfills the parameterization requirements of soft set and fuzzy soft set. FHS-set is projected to address the limitations of these models regarding the entitlement of multi-argument approximate function. This kind of function maps the sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its attribute-valued set that is missing in existing soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. As convexity has an essential function in optimization and control, pattern classification and recognition, image processing and in different fields of operation research, numerical analysis, etc. In order to tackle the various features of classical convexity (concavity) with uncertain environment of multi-argument approximate function, an articulate cum mathematical technique is utilized to develop a theoretical framework of convexity cum concavity on fuzzy hypersoft set which is more generalized and effective concept to deal with optimization relating problems. Moreover, some generalized properties like strictly convex (concave), strongly convex (concave), δ -inclusion and aggregation operations are established. The proposed study is authenticated with the provision of daily-life application based on proposed decision-making algorithm. Lastly, the features of proposed study are compared with the some existing relevant models to show its meritorious impact. [ABSTRACT FROM AUTHOR]

An editorial is presented on logic being applied in various science and engineering domains. Topics include considering new and recent developments in methodologies, techniques, and applications of Neutrosophic and plithogenic sets for various practical problems and demonstrating the challenging issues; and N-subalgebras on the algebraic structure being the quasi-subalgebra and vice versa by establishing a quasi-subalgebra of a Sheffer stroke BL-algebra.

A single-valued neutrosophic set is one of the advanced fuzzy sets that is capable of handling complex real-world information satisfactorily. A development of single-valued neutrosophic set and fuzzy bipolar set, called a bipolar neutrosophic set, was introduced. Distance measures between fuzzy sets and advanced fuzzy sets are important tools in diagnostics and prediction problems. Sometimes they are defined without considering the condition of the inclusion relation on sets. In decision-making applications, this condition should be required (here it is called the inference of the measure). Moreover, in many cases, a distance measure capable of discriminating between two nearly identical objects is considered an effective measure. Motivated by these observations, in this paper, a new distance measure is proposed in a bipolar neutrosophic environment. Furthermore, an entropy measure is also developed by the similarity between two sets of mutual negation. Finally, an application to medical diagnosis is presented to illustrate the effective applicability of the proposed distance measure, where entropy values are used to characterize noises of different attributes. [ABSTRACT FROM AUTHOR]

A Plithogenic Logical proposition P is a proposition that is characterized by many degrees of truth-values with respect to many corresponding attribute-values (or random variables) that characterize P. Each degree of truth-value may be classical, fuzzy, intuitionistic fuzzy, neutrosophic, or other fuzzy extension type logic. At the end, a cumulative truth of P is computed. [ABSTRACT FROM AUTHOR]

Uninorm generalizes the notion of t-norm and t-conorm in fuzzy logic theory. They are three increasing, commutative and associate operators having one neutral element. However, such specific value identifies the kind of operator it is; t-norms have the 1 as neutral element, t-conorms have the 0 and uninorms have every number lying between 0 and 1. Uninorms have been applied as aggregators in many fields of Artificial Intelligence and Decision Making. This theory has also been extended to the framework of interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and L-fuzzy sets. This paper aims to explore neutrosophic uninorms. We demonstrate that it is possible to define uninorms operators from neutrosophic logic. Additionally, we define neutrosophic implicators induced by neutrosophic uninorms. The combination of both, Neutrosophy and uninorms, enriches the applicability of uninorms operators due to the possibility of incorporating indeterminancy as part of the Neutrosophy contribution. [ABSTRACT FROM AUTHOR]

This article aims to propose an approach for determining reliability of information collected using questionnaires and bipolar neutrosophic sets. Bipolar neutrosophic sets use six membership functions that express the truth membership, the falsity membership, as well as the indeterminacy membership to the set and complementary set. Therefore, bipolar neutrosophic numbers may be suitable for applying in multi-criteria evaluation when a smaller number of complex evaluation criteria are used. Unfortunately, a significant number of membership functions make them somewhat complex for collecting data by surveying respondents. Using reliability of data decision-makers can identify respondents who did not want to participate in the survey, or did not understand the application of BNNs, and take appropriate action. The usability of the proposed approach is presented through two illustrative examples and conclusions were drawn based on obtained results. [ABSTRACT FROM AUTHOR]

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-sosophisticated distance measure between two SVNSs is defined by considering the crossassessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the new concept of Quadripartitioned Neutrosophic Pythagorean soft set with T, C, U, F as dependent neutrosophic components and have also discussed some of its properties. [ABSTRACT FROM AUTHOR]

Undoubtedly, most of the information conveyed is full of impreciseness or vagueness. In such situation, fuzzy set theory is a proper tool to handle these types of impreciseness or vagueness. Fuzzy numbers are also of different types based on the presence of uncertainty. Neutrosphic numbers are one type of fuzzy number that consists of three types of membership functions, namely, truth, indeterminacy and falsity. In fact, neutrosophic numbers are generalization of intuitionistic fuzzy numbers. These numbers might be used in decision making problems, where it is essential to rank those numbers. So, ordering of these numbers becomes a new trends with more challenges. In this paper, an innovative ranking approach of single‐valued neutrosophic number has been put forwarded. The method is based on value, ambiguity and θ function. Value and ambiguity are defined on three functions of the neutrosophic numbers. Further, the reliability of the proposed method is established by considering the reasonable properties of ranking method. One important aspect of ranking neutrosophic numbers is to consider the consistency in ordering the neutrosophic numbers and their corresponding images. It is worth to mention that the current approach consistently ranks the single‐valued neutrosophic numbers as well as their corresponding images. [ABSTRACT FROM AUTHOR]

In this paper, a new environment namely, intuitionistic fuzzy hypersoft set (IFHSS) is defined. We introduce some fundamental operators of intuitionistic fuzzy hypersoft sets such as subset, null set, absolute set, complement, union, intersection, equal set etc. Validity and application are presented with appropriate examples. For greater precision and accuracy, in the future, proposed operations in decision making processes such as personal selection, management issues and others will play a vital role. [ABSTRACT FROM AUTHOR]

The complex fuzzy soft set and its generalized hybrids are such effective structures which not only minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulfill all the parametric requirements of soft sets. This feature makes it a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set as it transforms the single attribute function into a multi-attribute function. This generalization demands an extension of complex fuzzy soft-like structures to hypersoft structure for more precise results. In this study, hybrids of hypersoft set with complex fuzzy set and its generalized structures i.e. complex intuitionistic fuzzy set and complex neutrosophic set, are developed along with illustrative examples to address the demand of literature. Moreover, some of their fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic operations i.e. compliment, union, intersection etc. are discussed. [ABSTRACT FROM AUTHOR]

The sociogram is a technique of sociometry widely used in the field of sociology due to its simplicity and effectiveness. The purpose of this method is the graphical visualization of the relationships among the members of a social group. The sociogram has been extended to the fuzzy framework to include uncertainty in the so-called fuzzy sociograms. However, there could be indeterminate relationships among some members of the group, because they have not experience in performing some activities together, although potentially either future links or disagreements could be established among them. In this paper, we propose a neutrosophic sociogram, which allows representing the indeterminacies in the relationships among some members of a group. The advantage of neutrosophic sociograms over fuzzy sociograms is that the representation and calculation considering indeterminacy, allow us to achieve greater accuracy in the results, and a greater approach to the potentialities of the group in terms of the future bond among the members. A hypothetical example is proposed to illustrate the applicability of the method. [ABSTRACT FROM AUTHOR]

Although the single valued neutrosophic sets (SVNSs) are effective tool to express uncertain information and are superior to the fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and q-rung orthopair fuzzy sets, there is not yet reported an operation which can provide desirable generality and flexibility under single valued neutrosophic environment, although many operations have been developed earlier to meet above such eventualities. So, the primary aim of this paper is to propose the concept of m-generalized q-neutrosophic sets (mGqNSs) as a further generalization of fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets and q-rung orthopair fuzzy sets, single valued neutrosophic sets, n-hyperspherical neutrosophic sets and single valued spherical neutrosophic sets. Under the m-generalized q-neutrosophic environment, we develop some new operational laws and study their properties. Using these operations, we define m-generalized q-neutrosophic weighted aggregation operators. The distinguished features of these proposed weighted aggregation operators are studied in detail. Furthermore, based on these proposed operators, a MADM (multi-attribute decision making) approach is developed. Finally, an illustrative example is provided to show the feasibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Plithogenic Hypersoft sets was introduced by Florentin Smarandache, who has extended crisp sets, fuzzy sets, intuitionistic sets, neutrosophic sets to plithogenic sets. The plithogenic sets considers the degree of appurtenance of the elements with respect to the attribute system. Smarandache has presented the classification of the plithogenic hypersoft sets and the applications of plithogenic fuzzy whole hypersoft sets in multi attribute decision making. Inspired by these research works, the concept of combined plithogenic hypersoft sets is introduced in this article. The representations of the degree of appurtenance of the elements determines the type of plithogenic hypersoft set, if it takes a combination of values then the new archetype of plithogenic hypersoft sets gets emerged into decision making scenario. This research work is put forth to project the realistic perception of the experts in the construction process of optimal conclusions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiat formal study of hypersoft sets. We first, present basic operations like union, intersection and difference of hypersoft sets; basic ingrediants for topological structures on the collection of hypersoft sets. Moreover we introduce hypersoft points in different envorinments like fuzzy hypersoft set, intuitionistic fuzzy hypersoft set, neutrosophic hypersoft, plithogenic hypersoft set, and give some basic properties of hypersoft points in these envorinments. We expect that this will constitue an appropriate framework of hypersoft functions and the study of hypersoft function spaces. Examples are provided to explain the newly defined concepts. [ABSTRACT FROM AUTHOR]

Neutrophic offsets are neutrosophic sets whose truth-values lie outside the interval [0, 1].Uninorms are aggregation operators defined in fuzzy logic to generalize t-norms and t-conorms. They satisfy the axioms of symmetry, associativity, monotony and the existence of a neutral element. Fuzzy uninorms have been generalized to intuitionistic fuzzy sets, neutrosophic sets, and neutrosophic offsets, which are called offuninorms in the latter case. This paper aims to demonstrate that offsets and offuninorms can be used in digital image processing, especially for image segmentation and edge detection, moreover algorithms and examples are also provided. [ABSTRACT FROM AUTHOR]

The single-valued neutrosophic set (SVNS) is an extension of the fuzzy set and intuitionistic fuzzy set. This is a useful tool to deal with uncertain and inconsistent information. In the information theory, the distance measure, entropy measure and similarity measures have an important role. Several entropy measures of SVNSs have been proposed and applied in many real problems. But they have some restriction in practice and in the academic study. The similarity measures induced from entropy were studied and gave interesting results. In this paper, we introduce a new entropy measure concept based on the SVNS, which overcomes the restriction of existing entropy measures. At the same time, we also investigate some similarity measures which are induced from new entropy measures and apply them to propose the multi-criteria decision making (MCDM) model in selecting the supplier. [ABSTRACT FROM AUTHOR]

Plithogenic Hypersoft sets (PHS) introduced by Smarandache are the extensions of soft sets and hypersoft sets and it was further protracted to plithogenic fuzzy whole Hypersoft set to make it more applicable to multi attribute decision making environment. The fuzzy matrix representation of the plithogenic hypersoft sets lighted the spark of concentric plithogenic hypergraph. This research work lays a platform for presenting the concept of concentric plithogenic hypergraph, a graphical representation of plithogenic hypersoft sets. This paper comprises of the definition, classification of concentric plithogenic hypergraphs, extended hypersoft sets, extended concentric plithogenic hypergraphs and it throws light on its application. Concentric Plithogenic hypergraphs will certainly open the new frontiers of hypergraphs and this will undoubtedly bridge hypersoft sets and hypergraphs. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce novel concepts of m-polar neutrosophic set (MPNS) and topological structure on m-polar neutrosophic set by combining the m-polar fuzzy set (MPFS) and neutrosophic set. Then, we investigate several characterizations of m-polar neutrosophic set and establish its various operations with the help of examples. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). We establish m-polar neutrosophic topology and define interior, closure, exterior, and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results with counter examples, which hold for classical set theory, but do not hold for m-polar neutrosophic set theory. We introduce a cosine similarity measure and a set theoretic similarity measure for m-polar neutrosophic sets (MPNSs). Furthermore, we present three algorithms for multi-criteria decision-making (MCDM) in medical diagnosis and clustering analysis under uncertainty by using m-polar neutrosophic sets (MPNSs) and m-polar neutrosophic topology. Lastly, we present advantages, validity, flexibility, and comparison of our proposed algorithms with the existing techniques. [ABSTRACT FROM AUTHOR]

In this article, we study neutrosophic fuzzy set and define the subtraction and multiplication of two rectangular and square neutrosophic fuzzy matrices. Some properties of subtraction, addition and multiplication of these matrices and commutative property, distributive property have been examined. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the concept of single-value neutrosophic irregular vertex coloring of SVNG. We determined the single-valued neutrosophic irregular chromatic number Xirv An for the graph with single value neutrosophic fuzzy set of vertices. [ABSTRACT FROM AUTHOR]

Neutrosophic sets are a generalization of the crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. This paper aims to characterize the solution of complex programming (CP) problem with imprecise data instead of its prices information. The neutrosophic complex programming (NCP) problem is considered by incorporating single valued trapezoidal neutrosophic numbers in all the parameters of objective function and constraints. The score function corresponding to the neutrosophic number is used to transform the problem into the corresponding crisp CP. Here, Lexicographic order is applied for the comparison between any two complex numbers. The comparison is developed between the real and imaginary parts separately. Through this manner, the CP problem is divided into two real sub-problems. In the last, a numerical example is solved for the illustration that shows the applicability of the proposed approach. The advantage of this approach is more flexible and makes a real-world situation more realistic. [ABSTRACT FROM AUTHOR]

Neutrosophic theory alleviates the ambiguity situation more effectively than fuzzy sets. Neutrosophic soft set deals with the combination of truth, indeterminacy and falsity membership. This provides a space for the convention with multi-aspect decision-making (MADM) problems that involve these combinations. The main aim of this paper is to provide a unique ranking for the alternatives to overcome the existing drawbacks in the said environment. Initially, a new score function and the weighted neutrosophic vector are discussed. Secondly, to show the supremacy of the proposed score function a comparison analysis is discussed between the existing score method and the proposed approach. Thirdly, algorithm and flowchart are discussed for the case study. Lastly, a new technique for ranking the alternatives is discussed which enables us to determine the unique highest score. The working model is illustrated with suitable examples to authenticate the tool and to demonstrate the effectiveness of the planned approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the new concept of Pythagorean neutrosophic set with T and F as dependent neutrosophic components [PNS]. Pythagorean neutrosophic set with T and F as dependent neutrosophic components [PNS] is introduced as a generalization of neutrosophic set (In neutrosophic sets, there are three special cases, here we take one of the special cases. That is, membership and non-membership degrees are dependent components and indeterminacy is independent) and Pythagorean fuzzy set. In PNS sets, membership, non-membership and indeterminacy degrees are gratifying the condition 0 = (uA(X))² + (𝜁A (X)) ² + (vA(X))² = 2 instead of uA(X) + 𝜁A (X) + vA(X) > 2 as in neutrosophic sets. We investigate the basic operations of PNS sets. Also, the correlation measure of PNS set is proposed and proves some of their basic properties. The concept of this correlation measures of PNS set is the extension of correlation measures of Pythagorean fuzzy set and neutrosophic set. Then, using correlation of PNS set measure, the application of medical diagnosis is given. [ABSTRACT FROM AUTHOR]

A divergence measure plays an important part in distinguishing two probability distributions and drawing conclusions based on that discrimination. In this paper, we proposed the concept of divergence measure of picture fuzzy sets. We also built some formulas of the proposed divergence measure of picture fuzzy sets anddiscussed some basic properties of this measure.Based on the proposedmeasure, we developed a multi-criteria decision-making algorithm. Finally, we applied the proposed multi-criteria decision-making algorithm in the medical diagnosis problem and the classification problem. [ABSTRACT FROM AUTHOR]

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having interior view). Thus, the speciality of PFWHSS is its presentation of an exterior and interior view of a situation simultaneously. Later, the PFWHSS is employed in development of multi attributes decision making scheme named as Frequency Matrix Multi Attributes Decision making scheme (FMMADMS). This innovative technique is not only simpler than any of the former MADM techniques, but also has a unique capability of dealing mathematically a variety of human mind psychologies at every level that are working in different environments (fuzzy, intuitionistic, neutrosophic, plithogenic). Besides, FMMADMS also provides the percentage authenticity of the final ranking which in itself is a new idea providing a transparent and unbiased ranking. Moreover, the new introduced idea of frequency matrix handles the ranking ties in the best possible way and has an ability to provide the authenticity comparative analysis of previously developed schemes. Lastly, application of this FMMADMS is described as a numerical example for a case of ranking and selecting the best alternative. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets are an extension of the intuitionistic fuzzy sets, and it also overcomes the limitations of the intuitionistic fuzzy sets. The entropy of a Pythagorean fuzzy set (PFS) is a measure of uncertainty related to the PFS. In this article, we exploit the concept of probability for defining the fuzzy entropy of Pythagorean fuzzy sets as an extension of the fuzzy entropy of Intuitionistic fuzzy sets (IFSs). Compared to some previous measures, the new measure is simpler, closer to the statistical significance and it reflects better fuzzy properties. After that, we give some numerical examples to compare our proposed entropy measure to some existing entropy of Pythagorean fuzzy sets. The results on numerical examples show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of a PFS and/or IFS. We also proposed a COPRAS multi-criteria decision-making method with weights calculated based on the proposed new entropy measure. The illustrated numerical example shows that the calculated results according to the proposed new method are similar to the calculation results according to some other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new correlation coefficient between intuitionistic fuzzy sets. We then use this new result to compute some examples through which we find that it benefits from such an outcome with some well-known results in the literature. As in statistics with real variables, we refer to variance and covariance between two intuitionistic fuzzy sets. Then, we determined the formula for calculating the correlation coefficient based on the variance and covariance of the intuitionistic fuzzy set, the value of this correlation coefficient is in [–1,1]. Then, we develop this direction to build correlation coefficients between the interval-valued intuitionistic fuzzy sets and apply it in the pattern recognition problem. Finally, we apply this correlation coefficient in clustering problem with intuitionistic fuzzy information. [ABSTRACT FROM AUTHOR]