Group decision making using circular intuitionistic fuzzy preference relations

Circular intuitionistic fuzzy sets (C-IFSs) emerge as a powerful extension of fuzzy and intuitionistic fuzzy sets (IFSs) to handle uncertain situations. Moreover, preference relations are widely used for solving group decision- making (GDM) problems. This paper defines circular intuitionistic fuzzy preference relations (C-IFPRs), using C-IFSs and preference relations. We define basic operations and aggregation operators for C-IFPRs. Several entropy measures for C-IFPRs are given and justified theoretically. A method is developed to generate the weights of decision-makers using entropy measures. New similarity measures are constructed to measure the resemblance between two C-IFPRs. On the other hand, an algorithm is proposed to improve the additive consistency of C-IFPRs. This algorithm guarantees the additive consistency of any C-IFPR, and once the consistency is achieved, it will hold even after further manipulations. Furthermore, a new method is developed to achieve an acceptable consensus level for GDM. It is based on similarity measures and aggregation operators. This method will guarantee that any sequence of C-IFPRs can achieve the group consensus. If the sequence is additively consistent, then this method will not disturb their consistency while achieving the group consensus. Additionally, it remains insensitive to similarity measures, and changing the similarity measure only affects the number of iterations to achieve group consensus. A TOPSIS-type selection process is extended to obtain a complete ranking, guaranteeing that the optimal solution is closest to the ideal solution and farthest from the worst option. In summary, this paper presents a GDM method leveraging C-IFPRs, an entropy-based weight generation method, additive consistency, a group consensus-reaching method, and a TOPSIS-type selection process. Numerical examples are provided to justify our developed approaches.