Concept Of Fuzzy Sets Research Articles

Modeling Imprecise and Bipolar Algebraic and Topological Relations using Morphological Dilations

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

The application of fuzzy set concept to assess service quality in tourist hotel settings

The application of fuzzy set concept to assess service quality in tourist hotel settings

The application of fuzzy set concept to assess service quality in tourist hotel settings

The Likert-type scale is commonly used in the hotel industry to measure service quality. This type of scale adopts classical sets concept defined by means of crisp boundaries, which does not allow for ambiguity in mathematical operations. In order to cope with the vague and subjective nature of linguistic measures, this study applied the fuzzy set concept. A translational model with 11 linguistic values and the equilateral triangular model were utilised to reduce the converting bias of service quality measures. While generating the overall rating of service quality in a hotel context, a weighted fuzzy membership function was considered to reduce the bias from midpoint misrepresentation and the bias from being unable to differentiate the dimensions based on importance to the respondent. This study contributes to the literature by using the fuzzy method to precisely represent the perceived service quality of hotel guests.

Material selection model using spherical Dombi fuzzy graph approach

In this research paper, the properties of Spherical Dombi Fuzzy Graph (SDFG) are discussed through examples. Moreover, we present a technique for selection of materials for a given technical unit based on Spherical Dombi Fuzzy Graph concept. The Spherical Dombi Fuzzy graph is developed considering material aspects and their priority for the application. We observed that the material selection model based on SDFG gives more space than fuzzy set, intuitionistic fuzzy set and picture fuzzy set concepts.

Rough topological space using equivalence relation

To generalise the basic rough set definitions, the topology induced by equivalence relations is used. The proposed topological structure opens the way for the implementation of a broad range of topological facts and techniques in the granular computing process, including the introduction of the definition of topological membership functions that incorporates the concept of rough and fuzzy sets. There is an overlap between rough set theory and several other theories dealing with incomplete knowledge

Decision-Making Based on q-Rung Orthopair Fuzzy Soft Rough Sets

Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S t S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF S t R) set (q-ROF S t RS). In addition, some averaging aggregation operators such as q-ROF S t R weighted averaging (q-ROF S t RWA), q-ROF S t R ordered weighted averaging (q-ROF S t ROWA), and q-ROF S t R hybrid averaging (q-ROF S t RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF S t R weighted geometric (q-ROF S t RWG), q-ROF S t R ordered weighted geometric (q-ROF S t ROWG), and q-ROF S t R hybrid geometric (q-ROF S t RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies.

New Methods of finding support planes of cut-level fuzzy power sets and Geometry of the convex fuzzy power sets

The concepts of the convex fuzzy power sets and crisply defined membership functions in fuzzy set theory are important to deeply analyze to look further for more precise solutions of the fuzzy mathematical programming problems. The Extension principle was defined in terms of the level cuts of the membership functions. The theorem of the decomposition proves the existence of the fuzzy power set as the union of all level cuts of membership function. The Convexity of the level cut fuzzy set was determined at the points of the universe, where the membership function is approximated. The Theorems of the convex and quasi-convex fuzzy sets extend and expand the extension principle to the higher quality to look for more precise solutions of fuzzy problems beyond the support planes. The Fuzzy geometry and topological categories researched further to arrive to the newest Lemma for the cyclic quadrilateral convex fuzzy sets. The analytical and graphical representation of modeling with membership functions type I through types 6 are investigated to the point to be highly recommended in engineering problems by using heuristic methods and models.

Decision-Making Approach with Fuzzy Type-2 Soft Graphs

Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles. We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples. The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems. We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services.

PYTHAGOREAN FUZZY MULTI SET AND ITS APPLICATIONS IN FISH FEED FOR INDIAN MAJOR CARP

Pythagorean fuzzy set is an extension of Intutionistic fuzzy set, which is more capable of expressing and handling the uncertainty under uncertain environments, so that it was broadly applied in various fields. In this paper, we explored the concept of Pythagorean fuzzy multi set (PFMS). We describe some basic set operations of Pythagorean fuzzy multi set and also, we proposed sine exponential distance function. Finally, through an illustrative example it is shown how the proposed distance works in decision-making problem.

Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

Measuring Given Partial Information about Intuitionistic Fuzzy Sets

Background: Measuring the information and removal of uncertainty are the essential nature of human thinking and many world objectives. Information is well used and beneficial if it is free from uncertainty and fuzziness. Shannon was the primitive who coined the term entropy for measure of uncertainty. He also gave an expression of entropy based on probability distribution. Zadeh used the idea of Shannon to develop the concept of fuzzy sets. Later on, Atanassov generalized the concept of fuzzy set and developed intuitionistic fuzzy sets. Purpose: Sometimes we do not have complete information about fuzzy set or intuitionistic fuzzy sets. Some partial information is known about them i.e either only few values of membership function <img src=image/13417006_01.gif> or non membership function <img src=image/13417006_02.gif> are known or a relationship between them is known or some inequalities governing these parameters are known. Kapur has measured the partial information given by a fuzzy set. In this paper, we have attempted to quantify partial information given by intuitionistic fuzzy sets by considering all the cases. Methodologies: We analyze some well-known definitions and axioms used in the field of fuzzy theory. Principal Results: We have devised methods to measure the incomplete information given about intuitionistic fuzzy sets. Major Conclusions: By devising the methods of measuring partial information about IFS, we can use this information to get an idea about the given set and use this information wisely to make a good decision.

Aggregation operators and VIKOR method based on complex q-rung orthopair uncertain linguistic informations and their applications in multi-attribute decision making

Complex q-rung orthopair uncertain linguistic set (CQROULS) is a combination of complex q-rung orthopair fuzzy set (CQROFS) and uncertain linguistic variable set (ULVS) as a proficient technique to express uncertain and awkward information in real decision theory. CQROULS contains uncertain linguistic variables, truth and falsity grades, which gives extensive freedom to decision makers for taking a decision as compared to CQROFS and their special cases. In this article, a new concept of fuzzy set, called CQROULS using CQROFS and ULVS is explored, and this can examine the qualitative assessment of decision makers and gives them extensive freedom in reflecting their belief about allowable truth grades. Based on the established operational laws and comparison methods for CQROULSs, the notions of complex q-rung orthopair uncertain linguistic weighted-averaging aggregation operator and complex q-rung orthopair uncertain linguistic weighted geometric aggregation operator are explored. Some special cases and the desirable properties of the explored operators are also established and studied. Additionally, the notion of VIseKriterijumska Optimizacija I KOmpromisno Resenje (VIKOR) method based on CQROULSs is explored, with the help of a numerical example, it is verified and also its comparative study is established. Moreover, based on the above analysis, we establish a method to solve the multi-attribute group decision making problems, in which the evaluation information is shown as CQROULNs. Finally, we solve some numerical examples using some decision making steps and explain the verity and proficiency of the explored operators by comparing with other methods, the advantages and graphical interpretation of the explored work are also discussed.

Triangular approximation of intuitionistic fuzzy numbers on multi-criteria decision making problem

Most of the engineering applications depend on incomplete and imprecise information which are represented by nonlinear mathematical functions for defining membership and nonmembership functions in intuitionistic fuzzy setup. Shuyang Li and Hongxing Li have studied the approximation of conventional intuitionistic fuzzy numbers in which the membership function is bounded and nonmembership function is unbounded in nature. The concepts of intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs) have bounded membership function and bounded nonmembership function. As the generalization of both IFSs and IVIFSs, the notion of intuitionistic fuzzy numbers of new type with bounded membership function and bounded nonmembership function has been introduced by Lakshmana et al. In this paper, the procedure for weighted triangular approximation of intuitionistic fuzzy number of new type is provided with some suitable illustrations. Moreover, some useful properties of the triangular approximation on intuitionistic fuzzy numbers have also been discussed.

Linguistic Interval-Valued Pythagorean Fuzzy Sets and Their Application to Multiple Attribute Group Decision-making Process

The paper’s aims are to present a novel concept of linguistic interval-valued Pythagorean fuzzy set (LIVPFS) or called a linguistic interval-valued intuitionistic type-2 fuzzy set, which is a robust and trustworthy tool, and to accomplish the imprecise information while solving the decision-making problems. The presented LIVPFS is a generalization of the linguistic Pythagorean fuzzy set, by characterizing the membership and non-membership degrees as the interval-valued linguistic terms to represent the uncertain information. To explore the study, we firstly define some basic operational rules, score and accuracy functions, and the ordering relations of LIVPFS with a brief study of the desirable properties. Based on the stated operational laws, we proposed several weighted averages and geometric aggregating operators to aggregate the linguistic interval-valued Pythagorean fuzzy information. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Finally, a multiple attribute group decision-making (MAGDM) algorithm is promoted to solve the group decision-making problems with uncertain information using linguistic features and the proposed operators. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Also, the illustration of the stated algorithm is given through several numerical examples and compared their performance with the results of the existing algorithms. Based on the stated MAGDM algorithm and the suitable operators, the decision-makers’ can be selected their best alternatives with their own attitude character towards optimism or pessimism choice. The presented LIVPFS is an extension of the several existing sets and is more generalized to utilize the uncertain and imprecise information with a wider range of information. Based on the presented aggregation operators, a decision-maker can select the desired one as per their choices to access the finest alternatives.

Fuzzy controlled humanoid robots: A literature review

Humanoid robots generated by inspiring by human appearances and abilities have became essential in human society to improve the quality of their life. All over the world, there have been many researchers who have focused on humanoid robots to develop the capabilities of humanoid robots. Generally, humanoid robot systems include mechanisms of decision making and information processing. Because of the uncertainty behind decision making and information processes, fuzzy sets are used most commonly. This study investigates a comprehensive literature review about humanoid robots that presents the recent technological developments and the theories associated with fuzzy set models. The basic principles and concepts of fuzzy sets for humanoid robots are presented.

Bi-parametric distance and similarity measures of picture fuzzy sets and their applications in medical diagnosis

The concept of picture fuzzy sets (PFS) is a generalization of ordinary fuzzy sets and intuitionistic fuzzy sets, which is characterized by positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measures and applications in data mining, medical diagnosis, decision making, and pattern recognition, several studies have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we propose new similarity measures for PFSs based on two parameters t and p, where t identifies the level of uncertainty and p is the Lp norm. The properties of the bi-parametric similarity and distance measures are discussed. We provide some counterexamples for existing similarity measures in the literature and show how our proposed similarity measure is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for medical diagnosis.

Thick Fuzzy Sets (TFSs) and Their Potential Use in Uncertain Fuzzy Computations and Modeling

This article aims at proposing the concept of thick fuzzy sets (TFSs). A TFS is based on the joint use of thick sets (TSs) and α-cuts concepts. A TFS is represented by a family of nested TSs. A TS is an uncertain set, which is represented by a pair of crisp sets (CSs). These CSs characterize the upper and lower bounds of the TS. Therefore, a TS can be regarded as an interval of CSs. In this framework, as a type-1 fuzzy set (T1FS) is regarded as a family of nested CSs, a TFS can be represented by a family of nested TSs. Furthermore, according to the vertical dimension α, a TFS can be regarded as an interval with T1FS bounds. The potentialities of the TFS concept have been validated using application examples where a real-world application for modeling the zone explored by an underwater robot is given.

Hesitant Bipolar-Valued Fuzzy Soft Sets and Their Application in Decision Making

As an extension of fuzzy sets, hesitant bipolar-valued fuzzy set is a new mathematical tool for dealing with fuzzy problems, but it still has the problem with the inadequacy of the parametric tools. In order to further improve the accuracy of decision making, a new mixed mathematical model, named hesitant bipolar-valued fuzzy soft set, is constructed by combining hesitant bipolar-valued fuzzy sets with soft sets. Firstly, some related theories of hesitant bipolar-valued fuzzy sets are discussed. Secondly, the concept of hesitant bipolar-valued fuzzy soft set is given, and the algorithms of complement, union, intersection, “AND,” and “OR” are defined. Based on the above algorithms, the corresponding results of operation are analyzed and the relevant properties are discussed. Finally, a multiattribute decision-making method of hesitant bipolar-valued fuzzy soft sets is proposed by using the idea of score function and level soft sets. The effectiveness of the proposed method is illustrated by an example.

Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras

In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.