Data envelopment analysis in hierarchical category structure with fuzzy boundaries

Data envelopment analysis (DEA) is used for the performance evaluation of a set of decision making units (DMUs). Such performance scores are necessary for taking managerial decisions like allocation of resources, improvement plans for the poor performers, and maintaining high efficiency of the leaders. In classical DEA, it is assumed that the DMUs are operating in a similar environment. But in practice, this assumption is normally broken as DMUs operate in a varied environment due to several uncontrollable factors like socio-economic differences, competitiveness in the region and location. In order to address this issue, categorical DEA was proposed for the construction of peer groups by creating crisp categories based on the level of competitiveness. However, such categorizations suffer from indeterminate factors, for example, human judgment and biases, linguistic ambiguity and vagueness. In this paper, we propose a more realistic DEA approach which is capable of handling categories defined in natural languages or with vague boundaries and generates efficiency as triangular fuzzy number. The analysis indicates that if a higher degree of fuzziness is allowed while defining the boundaries of the reference set, it results in (1) a compromise with the accuracy, signified by the spread of the fuzzy efficiency, (2) degradation of the quality, signified by the centre of the fuzzy efficiency, of the decision. Finally, the applicability of this approach has been demonstrated using public library data for different regions in Tokyo city. The sensitivity of the optimal decisions to the changes in fuzzy parameters has also been investigated.