Multiple criteria decision analysis based on Shapley fuzzy measures and interval-valued hesitant fuzzy linguistic numbers

Hesitant fuzzy sets (HFSs) are powerful tools in managing simultaneous sources of vagueness. Inspired by HFSs, interval-valued hesitant fuzzy linguistic sets (IVHFLSs) combine linguistic term sets and interval-valued hesitant fuzzy sets (IVHFSs) together to flexibly characterize uncertain information from simultaneous sources. The purpose of this paper is to investigate effective ways to aggregate such uncertain information and then apply them to multiple criteria decision analysis (MCDA). First, two interval-valued hesitant fuzzy linguistic Choquet integrals are proposed to characterize the interdependent characteristics between criteria. Then, based on the Shapley fuzzy measures, we develop two kinds of generalized interval-valued hesitant fuzzy linguistic Shapley Choquet integrals to globally characterize interactions between criteria combinations. A model designed to obtain the optimal Shapley fuzzy measures is then constructed. Furthermore, an approach to interval-valued hesitant fuzzy linguistic MCDA is developed based on the proposed aggregation operators. Finally, a numerical example and a detailed discussion are provided to illustrate the application of the proposed approach and to demonstrate its practicality and effectiveness, respectively.