Hesitant Fuzzy Multi-Criteria Group Decision Making with Unknown Weight Information

The hesitant fuzzy set permits the membership degree of an element to be a set of several possible values between 0 and 1, and is therefore an efficient tool for handling multi-criteria group decision making (MCGDM) problems in which experts hesitate between several values to assess an alternative. The aim of this paper is to study MCGDM problems in which the criterion values provided by experts take the form of hesitant fuzzy elements, and the weight information about both the decision makers and the criteria is unknown. By minimizing the divergence among the individual hesitant fuzzy decision matrices, we first establish a nonlinear optimization model to obtain an exact formula, from which the weights of decision makers can be derived. Then, based on all the individual hesitant fuzzy decision matrices, we construct a nonlinear optimization model to determine the weights of criteria by maximizing group consensus. After obtaining the weights of decision makers and criteria, a simple additive weighting operator is used to aggregate all the individual hesitant fuzzy decision matrices into the collective hesitant fuzzy decision matrix and is used to obtain the collective overall hesitant fuzzy values corresponding to each alternative. Moreover, all the above results are also extended to interval-valued hesitant fuzzy situations. Finally, we apply the developed models to an investment selection problem.