A Novel Method for Hesitant Fuzzy Multiple Attribute Group Decision Making with Incomplete Weight Information

Abstract

Aims: The aim of this paper is to develop a novel method for dealing with multiple attribute group decision making (MAGDM) problems with hesitant fuzzy information, in which the attribute values provided by the decision makers take the form of hesitant fuzzy elements (HFEs), the information about the weights of decision makers is unknown, and the information about attribute weights is incompletely known or completely unknown. Study Design: The developed method includes the following three stages. Place and Duration of Study: The hesitant fuzzy set (HFS), originally proposed by Torra and Narukawa, is an efficient tool to deal with situations in which experts hesitate between several possible values to evaluate the membership degree of an element to a given set. Methodology: The first stage establishes a quadratic programming model to determine the weights of decision makers by maximizing group consensus between the individual hesitant fuzzy decision matrices and the group hesitant fuzzy decision matrix. The second stage uses the maximizing deviation method to establish an optimization model, which derives the optimal weights of attributes under hesitant fuzzy environments. After obtaining the weights of decision makers and attributes through the above two stages, the third stage develops a hesitant fuzzy TOPSIS (HFTOPSIS) method to determine a solution with the shortest distance to the hesitant fuzzy positive ideal solution (HFPIS) and the greatest distance from the hesitant fuzzy negative ideal solution (HFNIS). Results: A practical example is provided to illustrate the proposed method. Conclusion: The comparison analysis with the other methods shows that the developed method has its great superiority in handling the MAGDM problems with hesitant fuzzy information.