Expanding Pythagorean fuzzy sets with distinctive radii: disc Pythagorean fuzzy sets

This article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of the circular intuitionistic fuzzy set model that improves its performance thanks to the acclaimed extension of intuitionistic fuzzy sets to Pythagorean fuzzy sets. Then, we generalize C-PFSs to produce the novel disc Pythagorean fuzzy sets (D-PFSs). The constituent elements of both C-PFSs and D-PFSs are circular Pythagorean fuzzy values, either with a common or a distinctive radius. We lay out some fundamental algebraic and arithmetic operations on D-PFSs (hence on C-PFSs), namely union, intersection, addition, multiplication, and scalar multiplication, and we explore the main features of these operations. We propose and investigate the properties of the novel circular Pythagorean fuzzy weighted average/geometric aggregation operators. The COmbinative Distance based ASsesment approach, which is based on the Hamming and Euclidean distances, is expanded to the D-PFS framework. To justify its implementability, we apply the new methodology to a case study (selection of the best supermarkets to buy fresh fruit for a hotel) and then we compare it to related solutions.

Automated summary

This article introduces the circular Pythagorean fuzzy set (C-PFS) model, which is a generalization of the circular intuitionistic fuzzy set model. The C-PFS model improves performance by extending intuitionistic fuzzy sets to Pythagorean fuzzy sets. The novel disc Pythagorean fuzzy sets (D-PFSs) are also introduced as a generalization of C-PFSs. The article discusses algebraic and arithmetic operations on D-PFSs and explores the properties of circular Pythagorean fuzzy weighted average/geometric aggregation operators. The COmbinative Distance based ASsesment approach is expanded to the D-PFS framework and applied to a case study.