Entropy measures for extended hesitant fuzzy linguistic term sets and their applications

Abstract

As a useful format of assessment, hesitant fuzzy linguistic term set (HFLTS) comes to the fore because of its wide applications in decision making. Extended hesitant fuzzy linguistic term set (EHFLTS) is a generalized form of HFLTS, and applied to collect the hesitant fuzzy linguistic information of a group. In this paper, we focus on the problem of how to measure the uncertain information of an EHFLTS. We first establish axiomatic definition of entropy for EHFLTS. Then we propose a series of entropy measures for EHFLTSs, which are also applicable for measure the uncertainty of HFLTSs. Compared with the entropy measures for HFLTSs provided by Farhadinia, the proposed entropy measures can measure both fuzziness and hesitation of an EHFLTS or HFLTS. Finally, we present a method, based on entropy and distance of EHFLTS, to determine the weights of the criteria for multi-criteria group decision making problem.