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In this paper, we introduce the concept of circular Pythagorean fuzzy set(value) (C-PFS(V)) as a new generalization of both circular intuitionisticfuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs)proposed by Yager. A circular Pythagorean fuzzy set is represented by a circlethat represents the membership degree and the non-membership degree and whosecenter consists of non-negative real numbers $\mu$ and $\nu$ with the condition$\mu^2+\nu^2\leq 1$. A C-PFS models the fuzziness of the uncertain informationmore properly thanks to its structure that allows modelling the informationwith points of a circle of a certain center and a radius. Therefore, a C-PFSlets decision makers to evaluate objects in a larger and more flexible regionand thus more sensitive decisions can be made. After defining the concept ofC-PFS we define some fundamental set operations between C-PFSs and propose somealgebraic operations between C-PFVs via general $t$-norms and $t$-conorms. Byutilizing these algebraic operations, we introduce some weighted aggregationoperators to transform input values represented by C-PFVs to a single outputvalue. Then to determine the degree of similarity between C-PFVs we define acosine similarity measure based on radius. Furthermore, we develop a method totransform a collection of Pythagorean fuzzy values to a PFS. Finally, a methodis given to solve multi-criteria decision making problems in circularPythagorean fuzzy environment and the proposed method is practiced to a problemabout selecting the best photovoltaic cell from the literature. We also studythe comparison analysis and time complexity of the proposed method.

Circular Pythagorean fuzzy sets and applications to multi-criteria decision making