Concept Of Intuitionistic Fuzzy Sets Research Articles

A Study of Multi-criterion Fuzzy Decision-making Methods: Recent Trends and Directions

A plausible soft computing model for addressing ambiguity and vagueness in decision-making circumstances is the concept of intuitionistic fuzzy sets (IFSs). Utilizing similarity-distance metrics, cases like diagnostic analysis, Finance and Investment, pattern recognition, Risk Analysis and Assessment, etc. have been investigated. Numerous methods of distance and similarity have been suggested and utilized to solve deciding circumstances. Although the existing similarity measures and their distance counterparts are fairly significant, they have certain accuracy and conceptual alignment issues that need to be addressed in order to improve output reliability. As a result, a unique similarity-distance technique is introduced in this paper. To demonstrate the benefits of the innovative similarity-distance strategy over related current approaches, a comparative analysis is presented. The theoretical and philosophical aspects of the approach are set aside, and the analysis is solely focused on the algorithmic (technical) point of view. Applying the ranking algorithm yields a solution. A comparative study is presented to illustrate the advantages of the suggested measures. The outcomes of applying the suggested similarity metrics are confirmed by a technique known as Topsis. The outcomes are more logical, consistent, and productive in a skeptical setting.

Intuitionistic fuzzy operations and operators: Some observations

Since its inception, the concept of intuitionistic fuzzy sets is getting popularity day by day. In addition to several operations, so many operators are there to excel the development of this thought. Few of such operators have been focused here. The key objective of this paper is to study those operators over intuitionistic fuzzy sets and to explore some major properties on it.

Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach

In this paper, we introduce collection of intuitionistic fuzzy sets as a new concept of intuitionistic fuzzy sets. In ordinary, universal set in intuitionistic fuzzy sets is classical set. So in this paper, we generalize the universal set as a collection or family of intuitionistic fuzzy sets. We also present intersection and union operation on collection of of intuitionistic fuzzy sets and show that the operations hold commutative, assosiative, idempotent, and De Morgan’s laws properties.

Development of intuitionistic fuzzy cost efficiency model in data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric linear programming (LP) based technique to measure the relative efficiencies of decision-making units (DMUs). The conventional DEA models assume that input-output data is crisp, which may not always be feasible in practical situations due to the presence of ambiguity and imprecision. Therefore, to handle uncertain and imprecise data, the concept of intuitionistic fuzzy sets (IFS) has been introduced. In this study, the relative efficiencies of DMUs with uncertain data will be determined. For this reason, the conventional cost efficiency (CE) model of DEA is extended to IF environment. Also, the lower and upper-cost efficiency models are developed using α-cut and β-cut approach. The data for inputs, outputs and input prices are considered intuitionistic fuzzy numbers (IFNs), in particular triangular intuitionistic fuzzy numbers (TIFNs). To demonstrate the practical application of the proposed intuitionistic fuzzy cost efficiency models (IFCEMs), a numerical example is presented.

Some new results on intuitionistic fuzzy operators

The concept of intuitionistic fuzzy sets is becoming very popular day by day among mathematicians and researchers from other areas of science. It has been noticed that some operators have very interesting properties in Intuitionistic fuzzy sets. That is why these properties are investigated in this study. New findings on equality are obtained and proved.

CO2 emission based GDP prediction using intuitionistic fuzzy transfer learning

The industrialization has been the primary cause of the economic boom in almost all countries. However, this happened at the cost of the environment, as industrialization also caused carbon emissions to increase exponentially. According to the established literature, Gross Domestic Product (GDP) is related to carbon emissions (CO2) which could be optimally employed to precisely estimate a country's GDP. However, the scarcity of data is a significant bottleneck that could be handled using transfer learning (TL) which uses previously learned information to resolve new tasks, more specifically, related tasks. Notably, TL is highly vulnerable to performance degradation due to the deficiency of suitable information and hesitancy in decision-making. Therefore, this paper proposes ‘Intuitionistic Fuzzy Transfer Learning (IFTL)’, which is trained to use CO2 emission data of developed nations and is tested for its prediction of GDP in a developing nation. IFTL exploits the concepts of intuitionistic fuzzy sets (IFSs) and a newly introduced function called the modified Hausdorff distance function. The proposed IFTL is investigated to demonstrate its actual capabilities for TL in modeling hesitancy. To further emphasize the role of hesitancy modelled with IFSs, we propose an ordinary fuzzy set (FS) based transfer learning. The prediction accuracy of the IFTL is further compared with widely used machine learning approaches, extreme learning machines, support vector regression, and generalized regression neural networks. It is observed that IFTL capably ensured significant improvements in the prediction accuracy over other existing approaches whenever training and testing data have huge data distribution differences. Moreover, the proposed IFTL is deterministic in nature and presents a novel way for mathematically computing the intuitionistic hesitation degree.

Intuitionistic Fuzzy Modulus Similarity Measure

The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.

Quantifying individual scientific output in terms of a new intuitionistic fuzzy sets based author-level metrics (IFALM)

The present paper proposes the idea of formulating a new author-level citation metrics, quantifying the individual’s scientific output, which uses the concept of intuitionistic fuzzy sets. This new metrics gives more visibility to the proportion of direct self-citations and hidden (co-author or collaborative) self-citations in the form of an intuitionistic fuzzy pair. Examples are given retrieving the necessary information from Scopus, one of the largest databases of peer-reviewed literature, which algorithmically enables retrieval of one’s citations including and excluding their own or their co-authors’ self-citations, as well as the calculation of three different values of one’s h-index with and without these respectively. Linear and triangular graphical representations are given, as well as comparisons with the concept proposed in 2005 by Jorge E. Hirsch, the now famous h-index, and ideas for future elaboration of the concept of the new intuitionistic fuzzy sets based author-level metrics, or shortly IFALM.

Robust intuitionistic fuzzy clustering with bias field estimation for noisy image segmentation

The concept of intuitionistic fuzzy set has been found to be highly useful to handle vagueness in data. Based on intuitionistic fuzzy set theory, intuitionistic fuzzy clustering algorithms are proposed and play an important role in image segmentation. However, due to the influence of initialization and the presence of noise in the image, intuitionistic fuzzy clustering algorithm cannot acquire the satisfying performance when applied to segment images corrupted by noise. In order to solve above problems, a robust intuitionistic fuzzy clustering with bias field estimation (RIFCB) is proposed for noisy image segmentation in this paper. Firstly, a noise robust intuitionistic fuzzy set is constructed to represent the image by using the neighboring information of pixels. Then, initial cluster centers in RIFCB are adaptively determined by utilizing the frequency statistics of gray level in the image. In addition, in order to offset the information loss of the image when constructing the intuitionistic fuzzy set of the image, a new objective function incorporating a bias field is designed in RIFCB. Based on the new initialization strategy, the intuitionistic fuzzy set representation, and the incorporation of bias field, the proposed method preserves the image details and is insensitive to noise. Experimental results on some Berkeley images show that the proposed method achieves satisfactory segmentation results on images corrupted by different kinds of noise in contrast to conventional fuzzy clustering algorithms.

Similarity-Distance Decision-Making Technique and its Applications via Intuitionistic Fuzzy Pairs

The idea of intuitionistic fuzzy sets (IFSs) is a reasonable soft computing construct for resolving ambiguity and vagueness encountered in decision-making situations. Cases such as pattern recognition, diagnostic analysis, etc., have been explored based on intuitionistic fuzzy pairs via similarity-distance measures. Many similarity and distance techniques have been proposed and used to solve decision-making situations. Though the existing similarity measures and their distance counterparts are somewhat significant, they possess some weakness in terms of accuracy and their alignments with the concept of IFSs, which needed to be strengthened to enhance reliable outputs. As a consequent, this paper introduces a novel similarity-distance technique with better performance rating. A comparative analysis is presented to showcase the advantages of the novel similarity-distance over similar existing approaches. Some attributes of the similarity-distance technique are presented. Furthermore, the applications of the novel similarity-distance technique in sundry decision-making situations are explored.

New Generalized Intuitionistic Fuzzy Divergence Measure with Applications to Multi-Attribute Decision Making and Pattern Recognition

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition, etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: The divergence measure method is used to measure the divergence between two given sets. In addition, the results of the other existing measures are also given to compare with the proposed measure. Results: It was observed that the proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real-world problems related to MADM and pattern recognition.

Orthopair indeterminate information expression, aggregations and multiattribute decision making method with indeterminate ranges

A neutrosophic number (NN) (d = µ + vI) can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I. Regarding the hybrid concept of intuitionistic fuzzy set (IFS) and NN, this study presents an orthopair indeterminate set (OIS), an orthopair indeterminate element weighted arithmetic averaging (OIEWAA) operator and an orthopair indeterminate element weighted geometric averaging (OIEWGA) operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms. Thus, a multiattribute decision making (DM) approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting. Finally, the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes (alternatives) in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.

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.

Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment

The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs). In this paper, the notions of linear Diophantine fuzzy soft rough sets (LDFSRSs) and soft rough linear Diophantine fuzzy sets (SRLDFSs) are proposed as new hybrid models of soft sets, rough sets, and LDFS. The suggested models of LDFSRSs and SRLDFSs are more flexible to discuss fuzziness and roughness in terms of upper and lower approximation operators. Certain operations on LDFSRSs and SRLDFSs have been established to discuss robust multi-criteria decision making (MCDM) for the selection of sustainable material handling equipment. For these objectives, some algorithms are developed for the ranking of feasible alternatives and deriving an optimal decision. Meanwhile, the ideas of the upper reduct, lower reduct, and core set are defined as key factors in the proposed MCDM technique. An application of MCDM is illustrated by a numerical example, and the final ranking in the selection of sustainable material handling equipment is computed by the proposed algorithms. Finally, a comparison analysis is given to justify the feasibility, reliability, and superiority of the proposed models.

An EDAS Method for Multiple Attribute Group Decision-Making under Intuitionistic Fuzzy Environment and Its Application for Evaluating Green Building Energy-Saving Design Projects

Multiple attribute group decision-making (MAGDM) methods have a significant influence on decision-making in a variety of strategic fields, including science, business and real-life studies. The problem of evaluation in green building energy-saving design projects could be regarded as a type of MAGDM problem. The evaluation based on distance from average solution (EDAS) method is one of the MAGDM methods, which simplifies the traditional decision-making process. Symmetry among some attributes that are known and unknown as well as between pure attribute sets and fuzzy attribute membership sets can be an effective way to solve MAGDM problems. In this paper, the classical EDAS method is extended to intuitionistic fuzzy environments to solve some MAGDM issues. First, some concepts of intuitionistic fuzzy sets (IFSs) are briefly reviewed. Then, by integrating the EDAS method with IFSs, we establish an IF-EDAS method to solve the MAGDM issues and present all calculating procedures in detail. Finally, we provide an empirical application for evaluating green building energy-saving design projects to demonstrate this novel method. Some comparative analyses are also made to show the merits of the method.

On Fuzzy $e$-open Sets, Fuzzy $e$-continuity and Fuzzy $e$-compactness in Intuitionistic Fuzzy Topological Spaces

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results related topological concepts. Several preservation properties and some characterizations concerning intuitionistic fuzzy $e$-compactness have been obtained.

A New Relationship Between Intuitionistic Fuzzy Sets and Genetics

Intuitionistic fuzzy sets represent a generalization of the concept of fuzzy sets and has many applications to different fields of science. This paper applies the concept of intuitionistic fuzzy sets to genetics. More precisely, we consider some examples of hypergroupoids associated to biological inheritance, construct sequences of join spaces and find their intuitionistic fuzzy grades.

Forward and reverse flows pricing decisions for two competing supply chains with common collection centers in an intuitionistic fuzzy environment

This paper studies the selling and the acquisition price decisions for the products of two partially overlapping competing supply chains in an intuitionistic fuzzy environment. In the forward flows, the supply chains are assumed to produce substitutable products and sell them in a duopoly marketplace. The reverse flows are also concentrated on collecting and recycling the used products. While regularly it is assumed that the structures of the competing supply chains are completely separated, this paper assumes that the supply chains benefit from the services of the same collection centers. Considering the collection centers and the two supply chains to act as three integrated entities having enough bargaining powers to affect the decisions of each other, this paper concentrates on investigating the effects of different power structure scenarios on the optimal pricing decisions made by all of the parties involved in the problem. Another important feature of this study is that it employs the concept of intuitionistic fuzzy sets to integrate uncertainties and impressions inevitable in real-world situations into the decision-making process. To achieve this purpose, first, a new credibility-based definition for the concept of intuitionistic fuzzy variables is provided. This concept is then employed in the process of developing the intuitionistic fuzzy pricing models. A new expected value operator is also defined which is employed to transform the credibility-based intuitionistic fuzzy programming problems into their crisp equivalents. A numerical example is employed to discuss the properties of the introduced concepts, providing some interesting managerial implications regarding the defined problem.

Pythagorean fuzzy CODAS and its application to supplier selection in a manufacturing firm

PurposeThe purpose of this paper is to develop the Pythagorean fuzzy extension of CODAS method.Design/methodology/approachSupplier selection is a critical issue for manufacturing companies since it is a multidimensional problem including several conflicting criteria. A suitable multi criteria decision making (MCDM) method that could consider vagueness and impreciseness in the assessments should be used for this kind of problems. Pythagorean fuzzy sets (PFSs) are characterized by a membership degree and a non-membership degree satisfying the condition that their square sum is equal to or less than 1. PFSs extend the concept of intuitionistic fuzzy sets (IFSs). COmbinative Distance-based Assessment (CODAS) method is relatively a new MCDM technique introduced by Keshavarz Ghorabaee et al. (2016).FindingsPythagorean fuzzy CODAS gives better results than ordinary fuzzy CODAS since it considers the hesitancy of decision makers and presents a larger space for membership and non-membership definition.Originality/valueThe value of this paper is the proposal of a new method to use for the solutions of MCDM problems under vagueness and impreciseness. To show validity and effectiveness of the proposed method, an application to the supplier selection problem is given.

The Basis and Coordinates in Intuitionistic Fuzzy Environment

In 1983, Atanassov extended the fuzzy set and originally introduced the concept of intuitionistic fuzzy set (IFS). The basic elements in every IFS are called intuitionistic fuzzy numbers, each of which consists of a membership degree, a non-membership degree and a hesitancy degree. Compared with the traditional fuzzy set, the IFS is more flexible and practical to deal with the ambiguity and uncertainty. In this paper, we first try to define the basis in intuitionistic fuzzy environment and then study some of its relevant properties. After that, we propose the coordinates based on the basis and present some theorems of the coordinates. Finally, we show how to find the smallest basis of any region.