scholarly journals New Similarity Measures of Intuitionistic Fuzzy Sets

2007 ◽  
Vol 11 (2) ◽  
pp. 202-209 ◽  
Author(s):  
Hassan Rezaei ◽  
◽  
Masao Mukaidono
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Suitable Combination ◽  
Thinking Process ◽  
Human Thinking ◽  
The Relationship

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.

A New Similarity Measure of Intuitionistic Fuzzy Sets Considering Abstention Group Influence and Its Applications

2016 ◽  
Vol 25 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Bei Zhou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Group A ◽  
Multicriteria Group Decision Making

AbstractThe issue of similarity measures of intuitionistic fuzzy sets (IFSs) is considered in this paper. Many existing similarity measures for two IFSs fail to take the abstention group influence into consideration and may lead to counterintuitive results in some cases. To deal with the problem, this paper first discusses the limitations of the existing similarity measures by some numerical examples, then, by considering the influence of abstention group, a new similarity measure of intuitionistic fuzzy sets is proposed, and the same numerical examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition, multicriteria group decision making, and medical diagnosis.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves 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 counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

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

2011 ◽  
Vol 219-220 ◽  
pp. 160-164 ◽  
Author(s):  
Yan Bing Gong
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

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.

Using the Similarity Measure Between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2018 ◽  
pp. 972-985
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

scholarly journals Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 437 ◽  
Author(s):  
Hui-Chin Tang ◽  
Shen-Tai Yang
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Test Problems ◽  
Number Of Components ◽  
Intuitionistic Fuzzy

This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to analyze their counterintuitive behaviors. The results indicate that all the distance-based similarity measures have some counterintuitive test problems. Furthermore, for the largest number of components of the distance-based similarity measure, four types of counterintuitive examples exist. Therefore, the counterintuitive behaviors are inevitable for the distance-based similarity measures between intuitionistic fuzzy sets.

scholarly journals Similarity Measures between Temporal Complex Intuitionistic Fuzzy Sets and Application in Pattern Recognition and Medical Diagnosis

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Mohammed M. Khalaf ◽  
Sayer Obaid Alharbi ◽  
Wathek Chammam
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Intuitionistic Fuzzy ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This work addresses the issue of similarity measures between two temporal complex Atanassov’s intuitionistic fuzzy sets, many measures of similarity between complex Atanassov’s intuitionistic fuzzy sets. What was proposed before did not consider the abstention group influence, which may lead to counterintuitive results in some cases. A new structure of temporal complex Atanassov’s intuitionistic fuzzy sets is obtained. This set is formally generalized from a conventional Atanassov’s intuitionistic complex fuzzy sets. Here we analyze the limitations of the existing similarity measures. Then, a new similarity measure of temporal complex Atanassov’s intuitionistic fuzzy sets is proposed and several numeric examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition and medical diagnosis.

scholarly journals Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 612
Author(s):  
Hui-Chin Tang ◽  
Kuan-Sheng Cheng
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Number ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Test Problems ◽  
Intuitionistic Fuzzy ◽  
General Test

This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.

Using the Similarity Measure between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2015 ◽  
Vol 9 (2) ◽  
pp. 24-36 ◽  
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

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