Fuzzy DEA

In more general cases, the evaluation data are often collected through investigation into the quality of the natural language such as “good,” “medium,” or “bad” rather than a specific case. That is, the data are fuzzy. We can find several fuzzy approaches to the efficiency assessment in the DEA literature. Cooper et al. [14, 15], one of the DEA initiators, introduced how to deal with imprecise data such as bounded data, ordinal data, and ratio bounded data in DEA. Kao and Liu [29] developed a method to find the membership functions of the fuzzy efficiency scores when some observations are fuzzy numbers. Entani et al. [17] proposed a DEA model with an interval efficiency which is obtained from the pessimistic and the optimistic viewpoints. Since possibility measure (Zadeh [46]) has been widely used in dealing with fuzzy data, many researchers have introduced it into DEA (Guo and Tanaka [24] and Lertworasirikul et al. [32]). However, the possibility measure has no self-duality property, which is needed both in theory and in practice. In order to define a self-dual measure, Liu and Liu [38] presented the concept of credibility measure in 2002. This chapter will give a brief introduction to fuzzy DEA based on credibility measure.