Multi criteria decision-making model using the circular Pythagorean fuzzy soft set model

Abstract

[ES]Lack of certainty is a major issue in decision-making, data analysis and modeling in many fields. Soft set theory has evolved into an effective method for addressing this issue, both due to its adaptability and its ability to blend with other models for the representation of uncertainty (inclusive of fuzzy sets and its extensions). Membership-based theories alone are incompatible with slackness in the evaluations, such as those that stem from measurement errors. This issue led to the appearance of interval-valued fuzzy sets (with only membership), and afterwards interval-valued intuitionistic fuzzy sets and circular intuitionistic fuzzy sets (with both membership and non-membership), plus other extensions that allow for wider domains of the evaluations. Circular Pythagorean fuzzy sets were defined with this motivation, and here we first combine them with soft set theory. In this setting, we propose novel score and accuracy functions based on optimistic and pessimistic perspectives. This is done with the help of a decision-maker-controlled parameter 𝜆 ∈ [0,1] that captures her/his approach to the problem. Furthermore, inspired by related models we define essential operations for the new framework, including complement, min-OR, max-OR, min-AND, max-AND, min-union, max-union, min-intersection, and max-intersection. All these tools allow us to extend decision-making strategies designed for Pythagorean fuzzy soft sets to the circular domain motivated by considerations of slackness. Finally, the study compares the proposed approach with circular intuitionistic fuzzy soft set based decision-making models to evaluate its effectiveness.