A Credibility Approach for Fuzzy Stochastic Data Envelopment Analysis (FSDEA)

It is well known that Data Envelopment Analysis (DEA) is a relative efficiency measurement tool, which uses optimization techniques to automatically calculate the weights assigned to the crisp deterministic multiple inputs and outputs of a set of the Decision Making Units (DMUs) being assessed. However, crisp deterministic data requirement delimits an application to the real world problems where some input or output measures likely are based on the value judgment of the decision makers. In this paper, the Fuzzy Stochastic Data Envelopment Analysis (FSDEA) model in the case of trapezoidal fuzzy numbers distributed with normal distribution in dual term is proposed, which is solved by two steps of transformation. First, the fuzzy deterministic DEA (FDDEA) model is converted by the concept of chance-constrained programming. Next, the credibility approach is used to convert a FDDEA model into a well-defined credibility programming model, in which fuzzy variables are replaced by expected credits.