Group decision making based on the relationships between the information measures for additive and multiplicative linguistic term sets

This paper investigates the systematic transformation of the information measures including the distance, similarity and entropy measures of linguistic term sets (LTSs) into each other. Firstly, we present the bilateral transforming approach of the distance measure into the similarity measure for both additive LTSs (ALTSs) and multiplicative LTSs. Then, the transformation of the distance measure into the entropy measure for ALTSs is investigated. This cycle of transformation is completed by investigating the transformation of the similarity measure into the entropy measure for ALTSs, and vice versa. In the sequel, in analogous to the results of linguistic arguments, the results of linguistic preference relations are achieved. Further, a rational approach is proposed to evaluate the relative weights of decision makers in the form of linguistic preference information.