Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making
Informatica (Netherlands), vol.34, no.4, pp.713-742, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 4
- Publication Date: 2023
- Doi Number: 10.15388/23-infor529
- Journal Name: Informatica (Netherlands)
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
- Page Numbers: pp.713-742
- Keywords: aggregation operators, circular Pythagorean fuzzy set, multi-criteria decision making
- Open Archive Collection: AVESIS Open Access Collection
- Ankara Yıldırım Beyazıt University Affiliated: Yes
Abstract
In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the non-membership degree and whose centre consists of non-negative real numbers μ and ν with the condition μ2 + ν2 ≤ 1. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain centre and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general triangular norms and triangular conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a C-PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method.