Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries

Data envelopment analysis (DEA) allows individual decision-making unit (DMU) to select the weights that are most favorable to them in calculating the ratio of the aggregated output to the aggregated input. The concept of the assurance region (AR) is restricting the ratio of any two weights to some range to avoid the evaluated DMUs from ignoring or relying too much on any criterion in evaluation. In this paper we develop a fuzzy DEA/AR method that is able to calculate the fuzzy efficiency score when the input and output data are represented as convex fuzzy numbers. Based on Zadeh’s extension principle, a pair of two-level mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy efficiency score. We transform this pair of two-level mathematical programs into a pair of conventional DEA/AR method to derive the bounds of the efficiency. The dual models of the fuzzy DEA/AR for efficiency improvement are also considered. To illustrate how the proposed method is applied, the measurement of the efficiency of the university libraries in Taiwan with fuzzy observations is exemplified.