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.In this 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.

► We modify the models in Liu and Chuang (2009) by adding the constraints of DMUr.
► We give a new proof of Proposition 1 in Liu and Chuang (2009).
► We propose a generalized fuzzy data envelopment model with assurance regions and the algorithm to obtain its lower and upper bounds at given levels.