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 calculated are also fuzzy. This paper devises a method to ranking the fuzzy efficiency scores without knowing the exact form of the membership functions of the fuzzy efficiencies. The idea is to apply maximizing and minimizing set method which is usually 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 in real world applications, the ranking of the twenty-four university libraries in Taiwan with fuzzy observations is exemplified.