Convex combination-based consensus analysis for intuitionistic fuzzy three-way group decision

Abstract

A three-way decision (3WD) with group consensus using intuitionistic fuzzy sets (IFSs) involves two pivotal decision steps: achieving a consensus of loss functions and determining the threshold pair in 3WD. We focus on these decision steps and propose a convex combination-based approach to a three-way intuitionistic fuzzy group decision (3WIFGD) considering a group consensus. First, a similarity measure between IFSs is introduced to define a group consensus index (GCI) for an expert group based on loss functions. Then, an automated algorithm is designed with the GCI-based convex combination strategy to improve the group consensus of loss functions. Moreover, we theoretically prove that the GCI in this algorithm is improved and even converges linearly to “1” as the iteration number increases. Second, based on the aggregated collective consensus loss functions, we construct the optimization model pair by extending the existing models and prove its unique solution, leading to the thresholds. Third, a two-decision-steps-based method for 3WIFGD is developed to capture the rules underlying a group consensus. Finally, an illustrative example and its related comparisons are demonstrated to show the validity of our method.