Fuzzy Data Envelopment Analysis (DEA)

Abstract

Data Envelopment Analysis (DEA is a well-known technique for efficiency analysis of business entities or organizations. The traditional DEA requires precise input and output data, while in real-world problems, available data is usually imprecise and is in the form of qualitative, linguistic data, e.g., "old' equipment and "high' inventory. "Fuzzy DEA' has integrated the concept of fuzzy set theory with the traditional DEA by representing imprecise and vague data with fuzzy sets. Fuzzy DEA models take the form of fuzzy linear programming models. Unfortunately, most fuzzy linear programming (FLP) models are not well defined due to ambiguity which arises in the ranking of fuzzy sets.

The objective of this dissertation is to develop solution approaches for solving fuzzy DEA models. Two main approaches are proposed, a possibility approach and a credibility approach. Both approaches resolve the problem of ranking fuzzy sets in fuzzy DEA models. We show that for the special case in which fuzzy membership functions of fuzzy data are trapezoidal both the possibility and credibility approaches transform fuzzy DEA models into linear programming models. Numerical examples are given to illustrate the approaches and results are compared with those obtained with other approaches.