Data envelopment analysis with missing data: an application to University libraries in Taiwan

In measuring the relative efficiencies of a set of decision making units (D MUs) via data envelopment analysis (DEA), detailed inputs and outputs are u sually involved. However, there are cases where some DMUs are unable to pro vide all the necessary data. This paper adopts the concept of a membership function used in fuzzy set theory for representing imprecise data. The smal lest possible, most possible, and largest possible values of the missing da ta are derived from the observed data to construct a triangular membership function. With the membership function, a fuzzy DEA model can be utilized t o calculate the efficiency scores. Since the efficiency scores are fuzzy nu mbers, they are more informative than crisp efficiency scores calculated by assuming crisp values for the missing data. As an illustration, the effici ency scores of the 24 University libraries in Taiwan, with three missing va lues, are calculated to show the extent that the actual amount of resources and services provided by each University is away from the technically effi cient amount of resources and services. This methodology can also be applie d to calculate the relative efficiencies of the DMUs with imprecise linguis tic data.