TOPSIS-Based Consensus Model for Group Decision-Making with Incomplete Interval Fuzzy Preference Relations

Due to the vagueness of real-world environments and the subjective nature of human judgments, it is natural for experts to estimate their judgements by using incomplete interval fuzzy preference relations. In this paper, based on the technique for order preference by similarity to ideal solution method, we present a consensus model for group decision-making (GDM) with incomplete interval fuzzy preference relations. To do this, we first define a new consistency measure for incomplete interval fuzzy preference relations. Second, a goal programming model is proposed to estimate the missing interval preference values and it is guided by the consistency property. Third, an ideal interval fuzzy preference relation is constructed by using the induced ordered weighted averaging operator, where the associated weights of characterizing the operator are based on the defined consistency measure. Fourth, a similarity degree between complete interval fuzzy preference relations and the ideal one is defined. The similarity degree is related to the associated weights, and used to aggregate the experts' preference relations in such a way that more importance is given to ones with the higher similarity degree. Finally, a new algorithm is given to solve the GDM problem with incomplete interval fuzzy preference relations, which is further applied to partnership selection in formation of virtual enterprises.