A new method for group decision making with incomplete fuzzy preference relations

This paper presents a new method to coping with group decision making with incomplete fuzzy preference information. To do this, it first defines an additively consistent index of fuzzy preference relations, and then gives a method to calculating the priority vector for additively consistent fuzzy preference relations. When the individual fuzzy preference relation is incomplete, a goal programming model is constructed, by which the missing values can be obtained. Then, an iterative approach to obtain the acceptably additive consistency of fuzzy preference relations is introduced. After that, an induced hybrid weighted aggregation (IHWA) operator is presented to aggregate the collective fuzzy preference relation. The main features of this aggregation operator are that the group consistency is no smaller than the highest individual inconsistency, and the group consensus is no smaller than the smallest consensus between the individual fuzzy preference relations. As a series of development, an algorithm based on the acceptable consistency and the group consensus is developed. Finally, three examples are given to show the efficiency and feasibility of the developed procedure, and comparisons are also offered.