Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations

Abstract

The aim of this paper is to investigate a novel approach to group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations, which can avoid information distortion and obtain more credible decision making results. An interval transform function is defined, which can transform an intuitionistic fuzzy preference relation into an interval multiplicative preference relation. Then, an interval transform function based data envelopment analysis model is developed to obtain the ranking vector of consistent intuitionistic fuzzy preference relation, in which each of the alternatives is viewed as a decision making unit. Moreover, for any intuitionistic fuzzy preference relations, we propose two DEA cross-efficiency models to get the cross-efficiency values of all alternatives, and we can calculate the normalized intuitionistic fuzzy priority weight vector of the intuitionistic fuzzy preference relation based on the cross-efficiency values. A goal programming model is investigated to derive the weight vector of decision makers. A step-by-step procedure for group decision making approach based on DEA cross-efficiency with intuitionistic fuzzy preference relations is presented. Finally, numerical examples are given to illustrate the validity and applicability of the proposed method. This is the first attempt of employing the DEA cross-efficiency to the group decision making with intuitionistic fuzzy preference relations.