Group decision making with hesitant fuzzy linguistic preference relations based on multiplicative DEA cross-efficiency and stochastic acceptability analysis

Abstract

The aim of this paper is to investigate a novel approach to group decision making (GDM) based on multiplicative DEA cross-efficiency and stochastic acceptability analysis with hesitant fuzzy linguistic preference relations (HFLPRs), which can avoid information distortion and obtain more credible decision-making results. First, a transform function is defined, which can extract effective information of the hesitant fuzzy linguistic term set (HFLTS) sufficiently. Then, an optimization model is proposed to derive the occurring probabilities of the elements in the HFLTS. It can avoid the normalization process of HFLPRs and simulate the element-selection process of decision makers (DMs). Moreover, a Maximum Log DEA Cross Efficiency model is proposed to evaluate the relative efficiency of each alternative from HFLPR. We further develop the stochastic weight space acceptability analysis method to solve the GDM problem and a step-by-step procedure 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 multiplicative DEA cross-efficiency to the GDM with HFLPRs.