scholarly journals The Fourth Axiom of Similarity Measures

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1735 ◽  
Author(s):  
Chun-Hsiao Chu ◽  
Chih-Ping Yen ◽  
Yi-Fong Lin
Keyword(s):  
Pattern Recognition ◽  
Fault Diagnosis ◽  
Correlation Coefficient ◽  
Similarity Measure ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Turbine Engine ◽  
Symmetric Structure ◽  
Source Paper ◽  
Weighted Correlation

In this research, the fourth axiom to improve the well-defined examination of similarity measures is studied, where the measures have a symmetric structure. We first provide a theoretic enhancement of three correlation coefficient similarity measures that were proposed by a source paper. Second, we use the same numerical example proposed by the source paper for pattern recognition problems to illustrate that the weighted correlation coefficient similarity measure is dependent on the set of weights. Finally, we demonstrate that the correlation coefficient similarity measure in the intuitionistic fuzzy set environment can address the issue of practical fault diagnosis when solving the turbine engine problems using similarity measures with symmetric characteristics.

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.

A New Similarity Measure of Picture Fuzzy Sets And Application in pattern recognition

2020 ◽  
pp. 5-18
Author(s):  
Ngoc Minh Chau, Nguyen Thi Lan, Nguyen Xuan Thao ◽  
Keyword(s):  
Pattern Recognition ◽  
Fault Diagnosis ◽  
Fuzzy Sets ◽  
Steam Turbine ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
The Novel ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. We apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

scholarly journals Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1371
Author(s):  
Shchur Iryna ◽  
Yu Zhong ◽  
Wen Jiang ◽  
Xinyang Deng ◽  
Jie Geng
Keyword(s):  
Fault Diagnosis ◽  
Correlation Coefficient ◽  
Triangular Fuzzy Number ◽  
Neutrosophic Set ◽  
Mechanical Equipment ◽  
Inaccurate Information ◽  
The Given ◽  
Set Correlation ◽  
Accuracy Degree ◽  
Weighted Correlation

With the increasing automation of mechanical equipment, fault diagnosis becomes more and more important. However, the factors that cause mechanical failures are becoming more and more complex, and the uncertainty and coupling between the factors are getting higher and higher. In order to solve the given problem, this paper proposes a single-valued neutrosophic set ISVNS algorithm for processing of uncertain and inaccurate information in fault diagnosis, which generates neutrosophic set by triangular fuzzy number and introduces the formula of the improved weighted correlation coefficient. Since both the single-valued neutrosophic set data and the ideal neutrosophic set data are considered, the proposed method solves the fault diagnosis problem more effectively. Finally, experiments show that the algorithm can significantly improve the accuracy degree of fault diagnosis, and can better satisfy the diagnostic requirements in practice.

scholarly journals Similarity measures for Fermatean fuzzy sets and its applications in group decision-making

2022 ◽  
Vol 11 (2) ◽  
pp. 167-180
Author(s):  
Laxminarayan Sahoo
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Future Research ◽  
Uncertain Information

The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and group decision making. Here, we investigate score based similarity measures of Fermatean fuzzy sets and scout the uses of FFSs in pattern recognition. Based on different types of similarity measures a pattern recognition problem viz. personnel appointment is presented to describe the use of FFSs and its similarity measure as well as scores. The counterfeit results show that the proposed method is more malleable than the existing method(s). Finally, concluding remarks and the scope of future research of the proposed approach are given.

scholarly journals Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

2021 ◽  
Author(s):  
Athira T M ◽  
Sunil Jacob John ◽  
Harish Garg
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Clustering Algorithm ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Soft Sets ◽  
Membership Value

Abstract Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure.

Monotonic Similarity Measures of Interval-Valued Fuzzy Sets and Their Applications

2017 ◽  
Vol 25 (04) ◽  
pp. 515-544 ◽  
Author(s):  
Guannan Deng ◽  
Lianlian Song ◽  
Yanli Jiang ◽  
Jingchao Fu
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Inclusion Measure ◽  
Monotonicity Properties ◽  
Degree Of Similarity ◽  
Interval Valued

A similarity measure is a measure that indicates the degree of similarity between two objects. The purpose of this work is to investigate the monotonicity properties and applications of similarity measures on interval-valued fuzzy sets. Through analyzing the intuitions of similarities, three kinds of monotonic similarity measures are defined. Furthermore, their properties and relationships with entropy and inclusion measure are investigated and discussed. Finally, some applications of the proposed monotonic similarity measures, such as pattern recognition, medical recognition, and medical diagnosis are presented.

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.

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.

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