GRA method for multiple criteria group decision making with incomplete weight information under hesitant fuzzy setting

This study develops an approach to investigate the multiple criteria group decision making (MCGDM) problems with hesitant fuzzy information, in which the criteria values take the form of the hesitant fuzzy elements, the information about criteria weights is incompletely known and the information about experts' weights is correlative. In this paper, we utilize the Shapley function to produce an evaluation of the marginal weight of each expert in decision making and aggregate the given decision information to get the overall preference value of each alternative by experts. In order to get the weight vector of the criteria, we establish an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method, by which the criteria weights can be determined. Then, based on the traditional GRA method, calculation steps for solving hesitant fuzzy MCGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.