Cross-efficiency intervals integrated ranking approach based on the generalized Fermat-Torricelli point

Abstract

As a significant extension of data envelopment analysis studies, cross-efficiency has been commenly adopted to rank the performances of decision-making units (DMUs). Interval cross-efficiency techniques can solve the nonuniqueness problem by considering all possible weight sets in weight space. Most existing cross-efficiency approaches employ the average cross-efficiency to aggregate the cross-efficiency matrix (CEM), but the consensus preferences among DMUs acquire little consideration. In this paper, we develop a new integrated ranking technique for cross-efficiency intervals. Cross-efficiency methods with crisp and interval input–output data are used to construct generalized interval CEMs. The cross-efficiency intervals are projected into two-dimensional coordinates, and the optimal rally point is generated using the plant growth simulation algorithm to solve the generalized Fermat-Torricelli problem. A possibility distribution function is applied to transform the aggregated interval CEMs, and then we obtain the ultimate cross-efficiency rankings of all DMUs. Two illustrations are provided to demonstrate the validity of the proposed approach.