Fuzzy Data Envelopment Analysis

摘要

Data Envelopment Analysis (DEA) is a well-known technique for efficiency analysis of business entities and organizations. While the traditional DEA requires precise input and output data, available data is usually imprecise and vague. "Fuzzy DEA" has emerged as an extension for assessing the efficiency under the complex and uncertain environment. It integrates fuzzy set theory with traditional DEA, representing imprecise data with fuzzy sets. However, the fuzzy DEA model takes the form of a fuzzy linear program which is not well defined due to the ambiguity in the ranking of fuzzy sets. In this paper, we review three approaches to resolve the ambiguity, a possibility approach, a necessity approach and a credibility approach. These three approaches transform fuzzy DEA models into well-defined mathematical programming models. The possibility approach transforms fuzzy DEA models into possibility DEA models by using possibility measures of fuzzy events (fuzzy constraints), while the necessity approach transforms fuzzy DEA models into necessity DEA models by using necessity measures of fuzzy events. The credibility approach transforms fuzzy DEA models into well-defined credibility programming models, in which fuzzy variables are replaced by "expected values" in terms of credibility measures. For the case in which membership functions are trapezoidal, the possibility, necessity and credibility programming models becomes linear programming models. Numerical examples are given to illustrate the approaches and results are compared with those obtained with alternative approaches.