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. This 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.