Multiplicative data envelopment analysis cross-efficiency and stochastic weight space acceptability analysis for group decision making with interval multiplicative preference relations

Abstract

To deal with group decision making (GDM) with interval multiplicative preference relations (IMPRs), this paper proposes a novel method based on multiplicative data envelopment analysis (DEA) cross-efficiency and stochastic weight space acceptability analysis. We first develop a multiplicative DEA model to evaluate the relative efficiency of all alternatives of a given multiplicative preference relation (MPR). Then, we present a method, free from consistency adjustment, to derive a priority vector using the multiplicative DEA cross-efficiency with respect to the given MPR. For GDM with IMPRs, we consider the decision makers’ weights as a uniform distribution for acceptability analysis. A modified unacceptability index is further defined to measure the unlikeliness for a particular alternative in a particular rank. Finally, we develop an assignment problem model to achieve an optimal ranking by minimizing the total rank unacceptability, and to compute the expected priority vector of all alternatives. Numerical examples are provided to show the applicability and justifications of the proposed GDM method.