1 research outputs found
Circular Pythagorean fuzzy sets and applications to multi-criteria decision making
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
center consists of non-negative real numbers and with the condition
. 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 center 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 -norms and -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 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