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Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making
Volume 34, Issue 4 (2023), pp. 713–742
Pub. online: 18 September 2023      Type: Research Article      Open accessOpen Access
Received
1 October 2022
Accepted
1 September 2023
Published
18 September 2023

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 ${\mu ^{2}}+{\nu ^{2}}\leqslant 1$. 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.

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Biographies

Bozyigit Mahmut Can
https://orcid.org/0000-0003-3676-0901
mcbozyigit@aybu.edu.tr

M.C. Bozyiğit graduated from Ankara University (Turkey), Faculty of Science, Department of Mathematics in 2017 with a bachelor’s degree. He received his master’s degree in 2020 from Ankara University. He has been working as a research assistant at Ankara Yıldırım Beyazıt University since 2019. His doctoral studies are supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK). His current research interests are functional analysis, real analysis, fuzzy measure and set theory, generalized Choquet integrals, triangular norms, aggregation operators, multi-criteria decision making.

Olgun Murat
https://orcid.org/0000-0002-8660-5435
olgun@ankara.edu.tr

M. Olgun was born in 1979 in Aksaray (Turkey). He graduated from Ankara University (Turkey), Faculty of Science, Department of Mathematics in 2001 with a bachelor’s degree. He completed his master’s degree in 2004 and his doctorate in 2010 at Ankara University, respectively. He started as an assistant professor at Ankara University in 2011. He received the title of associate professor in 2016. He is currently working as a professor at Ankara University. His research interests are fuzzy measure and set theory, fixed point theory, spectral theory, difference and functional equations, general topology, operator theory, and ordinary differential equations. He is married and has two children.

Ünver Mehmet
https://orcid.org/0000-0002-0857-1006
munver@ankara.edu.tr

M. Ünver has graduated from the Department of Mathematics, Ankara University (Turkey), in 2007. He finished his master’s education in Ankara University in 2009. He studied summability theory and Korovkin type approximation theory during his master’s studies. He got his PhD degree in mathematics from Ankara University in 2013. He studied summability theory, Korovkin type approximation theory. He worked as an assistant professor at Ankara University for about 2 years and he has been working as an associate professor at Ankara University since 2017. His current research interests are fuzzy measure and set theory, multicriteria decision-making, Korovkin type approximation theory, and summability theory.


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© 2023 Vilnius University
Open access article under the CC BY license.

Keywords
circular Pythagorean fuzzy set aggregation operators multi-criteria decision making

Funding
This research of Mahmut Can BOZYİĞİT has been supported by Scientific and Technological Research Council of Türkiye (TÜBİTAK) Program 2211/E.

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