Similarity Measure Of Intuitionistic Fuzzy Sets Research Articles

A novel entropy of intuitionistic fuzzy sets based on similarity and its application in finance

In this paper, we propose a new formula for the entropy based on similarity measures of intuitionistic fuzzy sets (IFS). The contribution of this work is the proof that the new formula satisfies all the conditions of entropy. The experimentation on some examples shows that the new entropy is useful. Besides, we use the new entropy and similarity measures to design an algorithm for ranking assets in stock markets. The numerical results on 5 benchmark data sets were reported. It points out that the entropy and the similarity measures of IFS may provide an alternative tool for solving portfolio selection problems.

An Application of Multi Criteria Decision Making: Ranking of School Success

Decision making is the action of choosing between two or more options. Multicriteria decision making is a well-known concept that aims to select the best solution among several alternatives in decision making. For this paper have been benefitted from similarity measure for intuitionistic fuzzy sets in multi criteria decision making problem. This application is a method that gives very important and rational results in decision making. In this paper; success ranking of schools has been researched in multi criteria decision making. The aim of this study is to propose an application multi criteria decision making in intuitionistic fuzzy sets. Also from year to year ranking of school success has been determined with multi criteria decision making. Annual change of success of each school has been investigated. This paper is the first research that evaluates with application and offers suggestions in education. This application has been implemented for the first time in Turkey to achieve more consistent and better results. This study is not an educational research, only is an application made in the field of intuitionistic fuzzy logic.

A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition

Among the most interesting measures in intuitionistic fuzzy sets (IFSs) theory, the similarity measure is an essential tool to compare and determine degree of similarity between IFSs. Although there exist many similarity measures for IFSs, most of them cannot satisfy the axioms of similarity measure or provide reasonable results. In this paper, a novel knowledge-based similarity/dissimilarity measure between IFSs is proposed. Firstly, we define a new knowledge measure of information conveyed by the IFS and prove some properties of the proposed knowledge measure. Based on the proposed knowledge measure of IFSs, we construct a novel similarity/dissimilarity measure between IFSs and prove some properties of the proposed similarity measure. Then we use some illustrative examples to show that the proposed measures, though simple in concept and calculus, can overcome the drawbacks of the existing measures. Finally, we apply the proposed similarity/dissimilarity measure between IFSs in the pattern recognition problems to demonstrate that the proposed measure is the most reliable to deal with the pattern recognition problem in comparison with the existing similarity measures.

A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix

As a generation of fuzzy set theory, intuitionistic fuzzy (IF) set theory has received considerable attention for its capability on dealing with uncertainty. Similarity measures of IF sets are used to indicate the degree of commonality between IF sets. Although several similarity measures for IF sets have been proposed in previous studies, some of those cannot satisfy the axiomatic definitions of similarity, or provide counter-intuitive cases. In this paper, a new similarity measure between IF sets is proposed. The definition of similarity matrix is also presented to depict the relations among more than two IF sets. It is proved that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counter-intuitive cases. Moreover, it is demonstrated that the proposed similarity measure can be applied to define a positive definite similarity matrix.

A hierarchy-based similarity measure for intuitionistic fuzzy sets

Due to some unreasonable results obtained from most current similarity measures for intuitionistic fuzzy sets (IFSs), we introduce a necessary condition to obtain a stronger definition of similarity measures for IFSs, and present a new similarity measure derived from a general idea of similarity measures for concepts on a lattice. In experiments, we focus our attention on two basic directions of performance evaluation: one is how much the proposed measure is reasonable and the other is how much accuracy the measure produces when it is applied to classification problems. The experimental results show that the proposed measure is reasonable and achieves a satisfactory performance on classification problems.

A New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognitions

Intuitionistic fuzzy sets (IFSs), proposed by Atanassov, have gained attention from researchers for their applications in various fields. Then similarity measures between IFSs were developed. In this paper, firstly, some existing measures of similarity are reviewed. Then a new similarity measure is proposed and the relationships between some similarity measures are proved. Finally, the similarity measures of IFSs is applied to pattern recognition and the proposed similarity measures can provide a useful way for measuring IFSs more effectively.

AN OVERVIEW OF DISTANCE AND SIMILARITY MEASURES OF INTUITIONISTIC FUZZY SETS

The Intuitionistic Fuzzy Sets (IFSs), originated by Atanassov [1], is a useful tool to deal with vagueness and ambiguity. In the short time since their first appearance, many different distance and similarity measures of IFSs have been proposed, but they are scattered through the literature. In this paper, we give a comprehensive overview of distance and similarity measures of IFSs. Based on the weighted Hamming distance, the weighted Euclidean distance, and the weighted Hausdorff distance, respectively, we define some continuous distance and similarity measures for IFSs. We also utilize geometric distance model to define some continuous distance and similarity measures for IFSs, which are the various combinations and generalizations of the weighted Hamming distance, the weighted Euclidean distance and the weighted Hausdorff distance. Then we extend these distance and similarity measures for Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs).

New Similarity Measures of Intuitionistic Fuzzy Sets

In this review of existing similarity measures of intuitionistic fuzzy sets (IFSs), we apply some numerical examples showing that not all existing similarity measures are effective and reasonable in some cases. We propose properties based on intuition and the human thinking process that should be satisfied by all dissimilarity and similarity measures, together with new similarity measures of IFSs that overcome drawbacks of existing measures. In examples, we compare the proposed similarity measures to existing measures and present two propositions on the relationship between similarity and dissimilarity measures of IFSs. We also propose that a suitable combination of similarity measures may be a similarity measure.