The Fuzzy Cross-Entropy for Picture Hesitant Fuzzy Sets and Their Application in Multi Criteria Decision Making

In this article, we exploit the cross-entropy of picture hesitant fuzzy set is established by distinguishing the cross-entropy of picture fuzzy set and hesitant fuzzy set. First, many measurement concepts are established and their basic properties are studied. Further, two measures, which are based on the established picture hesitant fuzzy cross-entropy, are established for evaluating multi-criteria decision making problems in the environment of picture hesitant fuzzy sets. For both approaches, an optimization model is pioneered to examine the weight vector for multi criteria decision making problems with incomplete information on criteria weights. In a last, we give an example to express practical and effectiveness. The comparison of the proposed measures with existing measures is also discussed.