Several Generalized Interval-Valued 2-Tuple Linguistic Weighted Distance Measures and their Application

With respect to interval-valued 2-tuple linguistic variables, this paper first defines a generalized distance measure. Then, several generalized interval-valued 2-tuple linguistic weighted distance measures are presented. To consider the interactions between elements in a set, three correlative weighted distance measures named the generalized interval-valued 2-tuple linguistic Shapley weighted distance measure, the generalized interval-valued 2-tuple linguistic ordered Shapley weighted distance measure, and the generalized interval-valued 2-tuple linguistic hybrid Shapley weighted distance measure are provided. Meanwhile, several special cases and desirable properties are considered. To obtain the weight vectors, models based on the Euclidean distance measure are constructed. Subsequently, an approach to pattern recognition and to multi-attribute decision making with interval linguistic preference information is developed, and the associated examples are offered to show their concrete application.