Circular intuitionistic fuzzy decision making and its application

Abstract

Circular intuitionistic fuzzy set (C-IFS) is introduced by Atanassov in 2020 as an extension of intuitionistic fuzzy sets. It is represented by a circle with a radius (r) of each element consist of degrees of membership and nonmembership. Several MCDM methods based on distance measures of C-IFS are already proposed in the literature. The primary objective of this study is the development, with the use of the C-IFS, of a new formulation of functions to form a novel C-IFS multi-criteria decision making (MCDM) method. In addition to the existing literature, this study contributes to circular intuitionistic fuzzy sets by proposing some formulations on radius calculation and a new defuzzification function for C-IFS. The optimistic and pessimistic points are also defined on the set to identify a novel score function and an accuracy function with decision-makers attitude (λ). When the perspective of the decision-maker (λ) approaches 1, it means that C-IFS is defuzzified close to its optimistic point, and when the perspective (λ) approaches 0, it is defuzzified close to the pessimistic point of C-IFS. With the use of these functions, a novel C-IFS MCDM method is presented based on criteria weighting and alternative ranking algorithms. This technique is applied to a supplier selection problem for a seamless supply chain network. A sensitivity analysis is also performed to test the effect of parameter changes on the final results. The findings of the study are compared with the results of a classical IFS-MCDM model. Since C-IFS is an extension of IFS, in addition to similar rankings, more precise results are obtained by considering the optimistic and pessimistic points by including the decision-maker attitude in the functions proposed for C-IFS. The study is a pioneer in the C-IFS literature by presenting C-IFS defuzzification function and a new C-IFS MCDM procedure.