An Approach to Multiple Attribute Group Decision Making under Hesitant Fuzzy Linguistic Environments with Incomplete Weight Information

As a combination of the fuzzy linguistic approach and the hesitant fuzzy set (HFS), hesitant fuzzy linguistic term set (HFLTS) is an efficient tool to deal with situations in which experts hesitate between several possible linguistic terms to assess the membership of an element in qualitative settings. In this paper, we develop a novel method for solving multiple attribute group decision making (MAGDM) problems with hesitant fuzzy linguistic information, in which the attribute values provided by the decision makers take the form of hesitant fuzzy linguistic term sets (HFLTSs), the information about the weights of decision makers is unknown, and the information about attribute weights is incompletely known or completely unknown. The developed method consists of three parts. The first one establishes a quadratic programming model based on the maximizing group consensus method, which can be used to determine the weights of decision makers. The second one uses the maximizing deviation method to establish an optimization model, from which the optimal weights of attributes can be derived. The third one extends the TOPSIS method to hesitant fuzzy linguistic environments and develops a hesitant fuzzy linguistic TOPSIS method, which determines a solution with the shortest distance to the hesitant fuzzy linguistic positive ideal solution (PIS) and the greatest distance from the hesitant fuzzy linguistic negative ideal solution (NIS). Moreover, a practical example is provided to illustrate the proposed method. Finally, the comparison analysis with the other methods shows that the developed method is very effective and appropriate for solving hesitant fuzzy linguistic MAGDM with incomplete weight information.