Parametric circular intuitionistic fuzzy information measures and multi-criteria decision making with extended TOPSIS

The representation of a circular intuitionistic fuzzy set (C-IFS) involves using a circle to symbolize the uncertainty associated with the membership and non-membership functions. A significant advantage of C-IFS is its ability to model the vagueness present in membership and non-membership degrees. This is accomplished through the structure of C-IFSs, which allows for the representation of information using points positioned on a circle with a defined center and radius. Using this structure, a C-IFS facilitates the making of more sensitive and nuanced decisions. In this study, a score function and an accuracy function are introduced to rank circular intuitionistic fuzzy values (C-IFVs). Then, we put forth novel parametric distance measures to calculate the difference between C-IFSs. This measure allows us to examine the impact of membership degree, non-membership degree, and radius on various applications. By observing these effects, we gain insights into the behavior and significance of these parameters in practical scenarios. We also give a similarity measure for computing the degree of similarity between C-IFSs. Furthermore, an extended version of the circular intuitionistic fuzzy Technique for Order of Preference by Similarity to Ideal Solution (C-IF TOPSIS) method is introduced by utilizing aggregation operators and distance measures. This extension incorporates distance measures and is harmonized specifically for C-IFSs. We apply this extended TOPSIS to a multi-criteria group decision making problem sourced from existing literature. Additionally, we evaluate sensitive analysis of proposed extended TOPSIS according to different parameters.