Fuzzy data envelopment analysis: A discrete approach

Abstract

Data envelopment analysis (DEA) as introduced by Charnes et al [3] is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on -cut. One drawback of the -cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the α-cut approach. We introduce the concept of "local α-level" to develop a multiobjective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

Data envelopment analysis with neutrosophic inputs and outputs

“…The use of this theory in DEA can be traced to Sengupta (). According to Hatami‐Marbini, Emrouznejad, and Tavana (), DEA approaches using fuzzy theory can be classified into four primary categories: (a) parametric approaches that convert a fuzzy DEA model into a parametric model depending on a parameter α level (Kao & Liu, ; 2000 b; ; Razavi, Amoozad, Zavadskas, & Hashemi, ; Zadeh, Firozja, & Erfani, ; Zerafat Angiz, Emrouznejad, & Mustafa, ); (b) possibility approaches that represent fuzzy variables by probability distributions (Lertworasirikul et al, ; Wang, Chuang, & Tsai, ); (c) ranking approaches, with the main objective of designing a fuzzy DEA model able to yield fuzzy efficiencies that can be ranked using different methods (Jahanshahloo et al, ); and (d) defuzzification approaches that try to first convert fuzzy values of inputs and outputs into crisp values then to solve the resulting DEA crisp model (Juan, ). Many other approaches have also been introduced to fuzzy DEA development (Wang et al, ; Zerafat Angiz, Emrouznejad, & Mustafa, ).…”

Data Envelopment Analysis to measure relative performance based on key indicators from a supply network with Reverse Logistics

“…DEA model calculates the most favorable weight for each DMU and then compares this weighting against the other DMUs of the system and maximizes the objective function, which finally determines the relative efficiency for that DMU. For [33]…”

A fuzzy data envelopment analysis framework for dealing with uncertainty impacts of input–output life cycle assessment models on eco-efficiency assessment

“…(2002), Hosseinzadeh et al, (2009) and Azadeh & Alem (2010). In a recent work, Angiz et al (2012) introduced a local α-cut level approach to measure the efficiency of DMUs with fuzzy data which is then used to improve a multi-objective linear programming. Similar to the previous literature, this study also utilizes α-cut level-based Fuzzy DEA approach to assess the sustainability performance of 33 U.S. food manufacturing sectors.…”

“…In this regard, it is important to note that the performance metric used, "SPI", is defined as the ratio of total production output to the overall environmental impact. In this context, utilizing Fuzzy DEA is the best way to deal with such multiple inputs with different units of measurement, scale differences, and uncertainties due to its robust applicability nature of dealing with multiple inputs and outputs (Angiz et al, 2012). A typical DEA model basically measures the efficiency (called SPI for the particular problem studied) by utilizing the normalized input(s) and the normalized output(s) as a single efficiency score via rigorous mathematical programming where the subjective weighting is not required (Tatari & Kucukvar, 2012).…”