A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures

With respect to hesitant fuzzy linguistic term sets, a distance measure that can be seen as an extension of some linguistic distance measures is presented. Then, two generalized hesitant fuzzy linguistic weighted distance measures named the generalized hesitant fuzzy linguistic weighted distance (GHFLWD) measure and the generalized hesitant fuzzy linguistic 2-additive Shapley weighted distance (GHFLASWD) measure are defined, by which the comprehensive attribute values can be obtained. To consider the importance of the ordered positions and their internal interactions, the generalized hesitant fuzzy linguistic 2-additive Choquet Shapley weighted distance (GHFLACSWD) measure and the generalized hesitant fuzzy linguistic 2-additive Shapley Choquet weighted distance(GHFLASCWD) measure are presented. To cope with the situation where the weight information is incompletely known, models for the optimal weight vectors are constructed. Meanwhile, an approach to multi-granularity decision making with hesitant fuzzy linguistic preferences is proposed. Finally, an example is provided to illustrate the concrete application of the proposed method.