Consensus of three-way group decision with weight updating based on a novel linguistic intuitionistic fuzzy similarity

Abstract

Three-way group decision-making is an important direction of study in the fields of three-way decision-making and granular computing and has received much attention from scholars in recent years. According to previous studies, three-way group-decision usually involves two pivotal processes: consensus reaching of collective loss functions in a group and the determination of both thresholds. To address both issues, this paper approaches from a novel perspective of weight updating rather than by opinion adjustments as in previous studies, and we propose a weight-updating-based three-way group decision method in linguistic intuitionistic fuzzy opinions. First, a linguistic intuitionistic fuzzy set (LIFS) is utilized to evaluate loss functions among experts due to its advantages in uncertain evaluations, and we define a θ-similarity measure between LIFSs by combining similarity and divergence information. Moreover, some properties of this measure are verified and an approach to calculate the initial weights of experts is explored based on the measure. Second, we use the measure to define a group consensus index, construct an optimal aggregation model and design a weight-updating-based algorithm for achieving consensus of collective loss functions, and prove a convergence of the algorithm. Third, via consensus loss functions, we establish a single optimization model to determine both thresholds of each object and develop a weight-updating-based consensus reaching method for three-way group decision with linguistic intuitionistic fuzzy opinions. Finally, an illustrative example and comparative experiments are conducted to show the validity of our method.