An induced OWA aggregation operator with dual preference setting for DEA cross-efficiency ranking

Cross-efficiency (CE) evaluation is an extension of the data envelopment analysis approach that allows decision making units (DMUs) to assess their peers by means of their own appreciation weights. As a result, each DMU is presented with a vector of CE scores, which need to undergo an aggregation operation to yield the ultimate ranking score. The aggregation is commonly carried out through an appropriate aggregation operator. In this paper, we propose an induced ordered weighted averaging (IOWA) operator with dual preference setting (2-IOWA) as a new aggregation device. The 2-IOWA aggregation novelty resides in its twined order inducing variables, which are defined by exploiting exclusively the appreciative properties of the CE matrix. The first-order inducing variable is the voting rank order that characterizes the preference voting system embedded within the CE matrix. The corresponding IOWA-level 1 aggregation produces a composite vote for each DMU by employing as arguments the individual votes assigned to it. The second-order inducing variable is represented by these composite votes, which are adopted to induce a common order on the rows of the CE matrix as a part of the IOWA-level 2 aggregation. The 2-IOWA aggregation process is conducted with OWA weights that are generated through different minimax disparity models by using different optimism level values in order to corroborate the influence of subjectivity on the structure of the ranking patterns besides evaluating the robustness of the proposed methodological framework.