Generalized Hesitant Fuzzy Generalized Shapley-Choquet Integral Operators and Their Application in Decision Making

In this paper, two generalized hesitant fuzzy generalized Shapley-Choquet integral operators are defined, which globally consider the importance of elements in a set, and the correlations among them. Some important special cases are examined. An improvement order relationship between hesitant fuzzy elements (HFEs) is introduced, and a new distance measure of HFSs is defined. This distance measure can calculate the distance between two HFEs with different lengths. If the information about the weights of attributes is incompletely known, the model for the optimal fuzzy measure on attribute set is established. As a series of development, an approach to hesitant fuzzy multi-attribute decision making with incomplete weight information is developed, and a practical example is provided to verify the developed approach and demonstrate its practicality and effectiveness.