Common-weights fuzzy DEA model in the presence of undesirable outputs with ideal and anti-ideal points: development and prospects

Abstract

Abstract In the literature, fuzzy arithmetic approach has been used for solving fuzzy data envelopment analysis (DEA) model in the presence of undesirable outputs by use of ideal and anti-ideal decision-making units (DMUs). In order to obtain the best and the worst fuzzy efficiencies, such an approach allows each DMU to choose the most favorable weights via optimizing its own evaluation that needs to solve various mathematical models. On the one hand, solving one mathematical model to find the best fuzzy efficiency and solving another mathematical model to find the worst fuzzy efficiency for each DMU increase the computational complexity significantly. On the other hand, the fully flexibility of weights leads to the different set of weights that may not be desirable. This paper proposes a common-weight method from two optimistic and pessimistic perspectives in fuzzy environment to determine the common sets of weights (CWS) to compute the best and the worst fuzzy efficiencies of all DMUs. The advantages of using common-weight DEA method based upon fuzzy arithmetic approach are reduction of the computational complexities and evaluation of equitably the best and the worst fuzzy efficiencies on the same base. The proposed approach first solves one linear programming model to compute each of the best and the worst fuzzy efficiencies of all DMUS, and then combines them to find a relative closeness index for the overall assessment. The developed approach is illustrated by a numerical example form the literature and the obtained results are compared with those from the existing ones.

Keywords

• Data envelopment analysis
• Undesirable outputs
• Common set of weights
• Fuzzy ideal and anti-ideal points