Fuzzy slack based measure of data envelopment analysis: A possibility approach

Abstract

Slack based measure (SBM) model of Data Envelopment Analysis (DEA) is very effective to evaluate the relative efficiency of decision making units (DMUs). It deals with the directly input excess and output shortfall to assess the effect of slacks on efficiency with common crisp inputs and outputs. In some cases, input and output data of DMUs can’t be precisely measured, so, the uncertain theory has played an important role in DEA. In these cases, the data can be represented as linguistic variable characterized by fuzzy numbers. This paper attempts to extend the traditional DEA model to a fuzzy framework, thus proposing a fuzzy SBM DEA model based on possibility approach to deal with the efficiency measuring problem with the given fuzzy input and output data. Finally, numerical examples are presented to illustrate the proposed fuzzy SBM model. By extending to fuzzy environment, the DEA approach is made more powerful for application.