A mathematical programming approach to fuzzy efficiency ranking

Data envelopment analysis is a widely applied approach for measuring the relative efficiencies of a set of decision-making units (DMUs) which use multiple inputs to produce multiple outputs. When some observations are fuzzy, the efficiencies become fuzzy as well. This paper devises a method to rank the fuzzy efficiency scores without knowing the exact form of the membership functions. The idea is to apply the maximizing set-minimizing set method, which is normally applied when membership functions are known. Via a skillful modeling technique, the requirement of the membership functions is avoided. The efficiency rankings are consequently determined by solving a pair of nonlinear programs for each DMU. To illustrate how the proposed method is applied, the ranking of the 24 university libraries in Taiwan with fuzzy observations is exemplified.