A new ranking method to fuzzy data envelopment analysis using hurwicz criterion

The basic DEA results group the DMUs into two sets: efficient set and inefficient set. However, decision-makers are always interested in a complete ranking beyond the dichotomized classification, which leads to the researches work of fully ranking methods in DEA. Most existing ranking methods assume that all inputs and outputs data are exactly known, but in real life the data can not be precisely measured. Thus this paper will give a new ranking method in DEA under fuzzy environment. The Hurwicz criterion is employed to rank all the DMUs, which attempts to find a middle ground between the distances to the efficient frontier and to the inefficient frontier. By varying the parameter in the Hurwicz criterion, the ranking method can present various forms. This method can rank all the DMUs including efficient ones and inefficient ones. Since the fuzzy models are too complex to compute in an accurate way, we will give its equivalent crisp models. Finally, we will provide a numerical example to illustrate the fuzzy ranking method.