Heterogeneous multi-attribute group decision making based on a fuzzy data envelopment analysis cross-efficiency model

Heterogeneous multi-attribute group decision making (HMAGDM) is a kind of complex decision making problem, which exists widely in reality. The purpose of this paper is to extend data envelopment analysis (DEA) for solving the HMAGDM problems whose attribute values include real numbers, intervals, intuitionistic fuzzy numbers, triangular fuzzy numbers, trapezoidal fuzzy numbers and linguistic variables. For this purpose, a method to HMAGDM based on a fuzzy DEA cross-efficiency model is proposed. In the proposed method, heterogeneous information is uniformly transformed into intervals, which are expressed as variables with unknown parameters. On this basis, a fuzzy DEA cross-efficiency model is established to calculate the individual cross-efficiency intervals of decision making units (DMUs). The model takes into consideration all possible attribute values of each DMU in the intervals, and obtains stable evaluation results through peer evaluation mode and iteration. Then, a maximizing group consensus model is established to calculate the weights of decision makers (DMs). Given the weights of DMs, the individual cross-efficiency intervals can be aggregated into the collective cross-efficiency interval, and DMU can be ranked based on this. An example of supplier selection is presented to illustrate the practicability and effectiveness of the proposed method.