Hesitant Fuzzy Linguistic Archimedean Aggregation Operators in Decision Making with the Dempster-Shafer Belief Structure

We propose a novel method for hesitant fuzzy linguistic decision making by utilizing Dempster-Shafer (D-S) theory of evidence. First, we propose some novel operations of hesitant fuzzy linguistic term sets (HFLTSs) on the basis of closed operations on linguistic 2-tuples and distribution linguistic average aggregation (DLAA) operators. These novel operations not only avoid information loss and operational results exceeding the boundary of linguistic term sets, but also make the aggregation results interpretable. Then, we define the hesitant fuzzy linguistic Archimedean weighted arithmetic mean (HFLAWAM) and hesitant fuzzy linguistic Archimedean weighted geometric mean (HFLAWGM) operators of HFLTSs. These two proposed operators are able to overcome the shortcomings of the existing approaches to multicriteria decision making (MCDM) with HFLTSs. Then, to take into account the novel operations of HFLTSs and the MCDM under uncertainty, we propose the belief structure-HFLAWAM (BS-HFLAWAM) and belief structure-HFLAWGM (BS-HFLAWGM) operators of HFLTSs. After that, we create an approach to handle the hesitant fuzzy linguistic MCDM problems in light of proposed operators. Finally, we apply the created approach to a MCDM problem regarding political management of a country.