Circular Intuitionistic Fuzzy ELECTRE III Model for Group Decision Analysis

Abstract

ELECTRE III is a well-established outranking relation model used to address the ranking of alternatives in multi-criteria and multi-actor decision-making problems. It has been extensively studied across various scientific fields. Due to the complexity of decision-making under uncertainty, some higher-order fuzzy sets have been proposed to effectively model this issue. Circular Intuitionistic Fuzzy Set (CIFS) is one such set recently introduced to handle uncertain IF values. In CIFS, each element of the set is characterized by a circular area with a radius, r and membership/non-membership degrees as the centre. This paper introduces CIF-ELECTRE III, an extension of ELECTRE III within the CIFS framework, for group decision analysis. To achieve this, we define extensions for the group decision matrix and group weighting vector based on CIFS conditions, particularly focusing on optimistic and pessimistic attitudes. These attitudinal characters of the group of actors are constructed using conditional rules to ensure that each element of the set falls within the circular area. Parameterized by $\alpha \in [0,1]$ for the net score degree, we conduct an extensive analysis of group decision-making between optimistic and pessimistic attitudes. To illustrate the applicability of the proposed model, we provide a numerical example of the stock-picking process. Additionally, we conduct a comparative analysis with existing sets and perform sensitivity analyses to validate the results of the proposed model.