Fuzzy data envelopment analysis models with assurance regions: A note

In a recent paper in this journal by Liu and Chuang [Liu, S. -T., & Chuang, M. (2009). Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries. Expert Systems with Applications, 36(2), 1105–1113]. Proposition 1 is proved for finding lower and upper bounds of the α-cut of E ∼ r . However, we find that the above proof omit the verification of constraints of assurance regions and the models (11) and (12) omit the constraints of DMUr, which makes it incredible. s paper, we correct the models and proof of Proposition 1 in Liu and Chuang (2009). We also propose a generalized fuzzy data envelopment model with assurance regions, whose lower and upper bounds at given levels could be obtained similarly.