Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures

In this paper, several new correlation coefficients of hesitant fuzzy sets are defined, not taking into account the length of hesitant fuzzy elements and the arrangement of their possible values. To address the situations where the elements in a set are correlative, several Shapley weighted correlation coefficients are presented. It is worth noting that the Shapley weighted correlation coefficient can be seen as an extension of the correlation coefficient based on additive measures. When the weight information of attributes is partly known, models for the optimal fuzzy measure on an attribute set are constructed. After that, an approach to clustering analysis and decision making under hesitant fuzzy environment with incomplete weight information and interactive conditions is developed. Meanwhile, corresponding examples are provided to verify the practicality and feasibility of the new approaches.