An integrated ranking approach using cross-efficiency intervals and the cumulative prospect theory

Abstract

The cross-efficiency (CE) intervals provide the decision maker (DM) with an effective way to ranking the decision making units (DMUs), and to some extents, resolve the possible non-uniqueness of CE scores. Thus, it is imperative to design an appropriate method to rank the DMUs by means of these CE intervals. However, the existing methods for aggregating the CE intervals are on the basis of standard expected utility theory (EUT), which ignores the fact that individual’s behavior may significantly deviate from the classical principle when facing risks. Instead, this paper incorporates the behavior decision theory into the aggregation process of CE intervals. In particular, we aggregate CE intervals based on the cumulative prospect theory (CPT), which can incorporate behavior features such as loss aversion into the decision making process. Then, to avoid potential strategic evaluation manipulation, we choose the reference point (or anchoring efficiency) by using a parameter concerning DM’s attitudes toward risks. Moreover, the cumulative distribution function of the weighting function is determined by requiring it only to satisfy a certain dominance relation. Finally, we derive the aggregated weights of each scenario with the similarity measure, which requires no subjective weight information determined by the DM, and we illustrate the proposed approach by using a numerical example and a real example applied to efficiency evaluation of 16 research institutes in Chinese Academy of Sciences (CAS).