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 Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Raja Noshad Jamil ◽  
Tabasam Rashid
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Energy Policy ◽  
Multicriteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Multicriteria Decision ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

scholarly journals An Exhaustive Study of Possibility Measures of Interval-Valued Intuitionistic Fuzzy Sets and Application to Multicriteria Decision Making

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Fatma Dammak ◽  
Leila Baccour ◽  
Adel M. Alimi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Possibility Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Matrix ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Exhaustive Study ◽  
Interval Valued

This work is interested in showing the importance of possibility theory in multicriteria decision making (MCDM). Thus, we apply some possibility measures from literature to the MCDM method using interval-valued intuitionistic fuzzy sets (IVIFSs). These measures are applied to a decision matrix after being transformed with aggregation operators. The results are compared between each other and concluding remarks are drawn.

Sign in / Sign up

Export Citation Format

Share Document