Achieving threshold consistency in three-way group decision using optimization methodology and expert-weight-updating-strategy

Abstract

How to improve and achieve a group consistency under three-way group decision is a key research issue that has recently attracted more and more attention. To deal with this issue, this paper proposes an expert-weight-updating-based approach to achieve a threshold consistency under three-way group decision with various opinions of linguistic intuitionistic fuzzy numbers. First, we use a linguistic intuitionistic fuzzy number (LIFN) to evaluate loss functions among experts due to its advantages in uncertain evaluations, and establish a fundamental model of decision-theoretic rough sets with different opinions of multiple experts. Then, we put forward a single optimization model that is an extension of our previous model, and utilize a mapping technique with such optimization methodology to generate numerical thresholds of individual experts. Second, we employ the normalized Hamming distance to define concepts of similarity measure and group consensus index based on individual thresholds. Then, we design a method to derive initial weights, a strategy to update weights of experts, and an expert-weight-updating-based algorithm to achieve a consensus of group thresholds. Third, via this algorithm, we develop a three-way group decision consensus achieving approach based on linguistic intuitionistic fuzzy opinions with multiple experts. Finally, some experiments and comparative analysis are performed to verify a convergence of our algorithm and the effectiveness of our approach.