Mohammad Izadikhah - Department of Mathematics, College of Science, Arak Branch, Islamic Azad University, P.O. Box: ۳۸۱۳۵/۵۶۷, Arak, Iran
Dimitris K. Despotis - Department of Informatics, University of Piraeus, Greece

Wang et al. (۲۰۰۵) proposed a pair of data envelopment analysis (DEA) models to deal with the efficiency assessment of decision-making units (DMU) in the presence of interval input/output data. Their approach was developed with reference to an earlier approach proposed by Despotis and Smirlis (۲۰۰۲) for the same problem. Given that the input/output data are given as interval numbers, the efficiency scores are interval measures as well. In such a setting, both approaches provide lower and upper bounds for the efficiency scores. Wang et al. (۲۰۰۵) claim that the lower and upper bounds calculated in Despotis and Smirlis (۲۰۰۲) are incorrect. Then, they present different models to calculate the true bounds. In this paper, we counter-argue their claim and we show that the Despotis and Smirlis bounds are correct and those provided in Wang et al. are estimated in a manner that they fail to satisfy an obvious property that they should possess. We illustrate our arguments with a counterexample that was originally used in Wang et. al (۲۰۰۵).

Data envelopment analysis, Interval data, interval efficiency