Some Trigonometric Similarity Measures Based on the Choquet Integral for Pythagorean Fuzzy Sets and Applications to Pattern Recognition

2021 ◽  
pp. 83-106
Author(s):  
Ezgi Türkarslan ◽  
Murat Olgun ◽  
Mehmet Ünver ◽  
Şeyhmus Yardimci
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Choquet Integral ◽  
Similarity Measures ◽  
Pythagorean Fuzzy Sets

scholarly journals SIMILARITY MEASURES OF PYTHAGOREAN FUZZY SETS WITH APPLICATIONS TO PATTERN RECOGNITION AND MULTICRITERIA DECISION MAKING WITH PYTHAGOREAN TOPSIS

2021 ◽  
Author(s):  
Zahid Hussain
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Multicriteria Decision Making ◽  
Linguistic Variables ◽  
Multicriteria Decision ◽  
Pythagorean Fuzzy Sets ◽  
Rényi Divergence

The construction of divergence measures between two Pythagorean fuzzy sets (PFSs) is significant as it has a variety of applications in different areas such as multicriteria decision making, pattern recognition and image processing. The main purpose of this study to introduce an information-theoretic divergence so-called Pythagorean fuzzy Jensen-Rényi divergence (PFJRD) between two PFSs. The strength and characterization of the proposed Jensen-Rényi divergence between Pythagorean fuzzy sets lie in its practical applications which are very closed to real life. The proposed divergence measure is utilized to induce some useful similarity measures between PFSs. We apply them in pattern recognition, characterization of the similarity between linguistic variables and in multiple criteria decision making. To demonstrate the practical utility and applicability, we present some numerical examples related to daily life with the construction of Pythagorean fuzzy TOPSIS (Techniques of preference similar to ideal solution). Which is utilized to rank the Belt and Road initiative (BRI) projects. Our numerical simulation results show that the suggested measures are well suitable in pattern recognition, characterization of linguistic variables and multi-criteria decision-making environment.

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 New Similarity Measures of Pythagorean Fuzzy Sets and Their Applications

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 138192-138202 ◽  
Author(s):  
Qiang Zhang ◽  
Junhua Hu ◽  
Jinfu Feng ◽  
An Liu ◽  
Yongli Li
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measures ◽  
Pythagorean Fuzzy Sets

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.

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.

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