Linguistic group decision making: Axiomatic distance and minimum cost consensus

Abstract

The axiomatic distance-based method is a powerful tool to aggregate individual preferences, and the extant axiomatic distance-based aggregation methods are with regard to individual numerical preferences. However, in some real-world decision problems with qualitative aspects, it is more convenient and natural for individuals to express their preferences through linguistic terms rather than through numerical values. Therefore, in this paper, we propose axiomatic distance in the linguistic context based on ordered linguistic term sets to aggregate individual linguistic preferences. Specifically, we provide some natural axioms on the distance measure among linguistic preferences. We then prove that there exists a unique distance function that satisfies all the proposed axioms. Based on the axiomatic distance function, we aggregate individual linguistic preferences into the group linguistic preference, which minimizes the total distance among individual linguistic preferences. Furthermore, we present a novel consensus measure based on the unique axiomatic distance and develop a minimum cost consensus model to obtain the optimal adjusted linguistic preference, which serves as a reference for the moderator to persuade individuals to modify their linguistic preferences.