Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making

• We introduce a family of novel distance and similarity measures for HFLTSs.
• We develop a cosine-distance-based HFL-TOPSIS method.
• We develop a cosine-distance-based HFL-VIKOR method.
• We use a numerical example to illustrate the proposed methods.

Qualitative and hesitant information is common in practical decision making process. In such complicated decision making problem, it is flexible for experts to use comparative linguistic expressions to express their opinions since the linguistic expressions are much closer than single or simple linguistic term to human way of thinking and cognition. The hesitant fuzzy linguistic term set (HFLTS) turns out to be a powerful tool in representing and eliciting the comparative linguistic expressions. In order to develop some approaches to decision making with hesitant fuzzy linguistic information, in this paper, we firstly introduce a family of novel distance and similarity measures for HFLTSs, such as the cosine distance and similarity measures, the weighted cosine distance and similarity measures, the order weighted cosine distance and similarity measures, and the continuous cosine distance and similarity measures. All these distance and similarity measures are proposed from the geometric point of view while the existing distance and similarity measures over HFLTSs are based on the different forms of algebra distance measures. Afterwards, based on the hesitant fuzzy linguistic cosine distance measures between hesitant fuzzy linguistic elements, the cosine-distance-based HFL-TOPSIS method and the cosine-distance-based HFL-VIKOR method are developed to dealing with hesitant fuzzy linguistic multiple criteria decision making problems. The step by step algorithms of these two methods are given for the convenience of applications. Finally, a numerical example concerning the selection of ERP systems is given to illustrate the validation and efficiency of the proposed methods.