Measuring Cost Efficiency with New Fuzzy DEA Models

In conventional cost efficiency models, input and output data and their corresponding input prices are fundamentally known for each decision-making unit. However, the observed values of the input and output data in real problems are sometimes imprecise. This study shows that the cost efficiency evaluation method can be improved to account for situations where input–output data and their corresponding input prices are fuzzy numbers. A new fuzzy cost-minimizing model known as a possibilistic linear programming problem is proposed to evaluate the cost efficiency. In this model data information is considered as triangular fuzzy numbers. Using the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-level-based approach, the model is transformed into an interval programming problem which is solved as a crisp parametric linear programming model. In addition, new definitions of the fuzzy cost efficiency and cost efficient unit are suggested. Finally, a numerical example is presented to illustrate the proposed method.