A General Framework of Dealing with Qualitative Data in DEA: A Fuzzy Number Approach

Abstract

The original DEA models only deal with quantitative data because the algebraic operations on qualitative data are meaningless. This chapter provides the framework of dealing with qualitative data in DEA through fuzzy numbers. At first, use fuzzy numbers representing qualitative data. Then apply sets of two-level mathematical programing to implement fuzzy extension principle to crisp DEA model to find α-cuts of leveled fuzzy efficiency based on crisp observations and α-cuts of fuzzy factors. Adequate number of α-cuts determines the fuzzy efficiency. Furthermore, to provide persuadable fuzzy numbers representing qualitative data, use DEA models as experts to integrate objective production data and subjective information to generate possible values of qualitative data. Based on possible values of qualitative data, the shapes of fuzzy numbers are determined. To increase readability of fuzzy efficiency for most decision-makers, apply K-medoids clustering method along with Hausdorff distances to convert these efficiencies into qualitative efficiencies. Finally, a case of university performance evaluation demonstrates the framework.