A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry

Data envelopment analysis (DEA) is amathematical programmingapproach for evaluating the relative efficiency of decision making units (DMUs) in organizations. The conventionalDEAmethods require accuratemeasurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are often imprecise or vague. Fuzzy set theory is widely used to quantify imprecise andvaguedata inDEAmodels. In this paper,wepropose a four-step bounded fuzzy DEA model, where the inputs and outputs are assumed to be fuzzy numbers. In the first step, we create a hypothetical fuzzy anti-ideal DMU and calculate its best fuzzy relative efficiency. In the second step, we propose a pair of fuzzy DEAmodels to obtain the upperand the lower-bounds of the fuzzy efficiency, where the lower-bound Communicated by Jyh-Horng Chou. A. Hatami-Marbini Louvain School ofManagement, Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, L1.03.01, 1348 Louvain-la-Neuve, Belgium M. Tavana (B) Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, USA e-mail: [email protected] URL: http://www.tavana.us M. Tavana Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098 Paderborn, Germany K. Gholami Department of Science, Islamic Azad University, Bushehr Branch, Bushehr, Iran Z. G. Beigi Department of Mathematics, Islamic Azad University, Mabarakeh Branch, Isfahan, Iran