Linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision-making

As a generalization of hesitant fuzzy sets (HFSs) and hesitant fuzzy linguistic term sets (HFLTSs), linguistic hesitant fuzzy sets (LHFSs) establish a proper interpretation of the hesitancy, inconsistency and uncertainty of experts in evaluating decision alternatives. In this paper, based on the cloud model, we discuss multiple attribute decision-making problems with linguistic hesitant fuzzy information. To extend the applicability of LHFSs, we introduce the concept of a comprehensive cloud of LHFSs that is based on which form of LHFSs with different length can be unified. Utilizing the comprehensive cloud, we define the distance measure between two LHFSs, which makes the support measure of two LHFSs possible. By extending the power operators to the linguistic hesitant fuzzy environment, a series of linguistic hesitant fuzzy power aggregation operators are established. We also study the properties and applications of these aggregation operators and develop two approaches for linguistic hesitant fuzzy multiple attribute decision-making. Finally, two practical examples are given to demonstrate the applicability and effectiveness of the proposed approach.