Fuzzy data envelopment analysis (DEA): Model and ranking method

Abstract

a b s t r a c tData Envelopment Analysis (DEA) is a very effective method to evaluate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.

Scale efficiency with fuzzy data

“…Some researchers have proposed several fuzzy models to evaluate the efficiency of DMUs with fuzzy data (Agarwal, 2010(Agarwal, , 2014a(Agarwal, , 2014bGuo and Tanaka, 2001; Kao and Liu, 2000;Liu and Chang, 2009;Sengupta, 1992;Saati and Memariani, 2009;Wen and Li, 2009;Lertworasirikul et al, 2003aLertworasirikul et al, , 2003b. This study extended the credibility approach to solve fuzzy BCC DEA model and measure the scale efficiency with fuzzy data.…”

Efficiency evaluation of customer satisfaction index in e-banking using the fuzzy data envelopment analysis

“…In recent years, the use of qualitative and imprecise data in DEA model is the most important challenge of researchers. One of the options discussed in this context is the use of fuzzy set theory (Wen & Li, 2009;Zerafat Angiz et al, 2012).…”

Evaluation of Supply Chain of a Shipping Company in Iran by a Fuzzy Relational Network Data Envelopment Analysis Model

“…The optimal value of z hj is achieved by substituting this parameter into Models (33) and (34). After solving Model (35), the optimal values of reduced costs of s x i , s z h , and s y are the values of multipliers v i , w h , and u , respectively.…”

“…Fuzzy sets, which were introduced by Zadeh [25], are one of the common methods for solving DEA with imprecise data. The applications of fuzzy set theory in DEA are usually divided into four categories [24,26]: tolerance approach [27,28], -level based approach [29,30], fuzzy ranking approach [31,32], and possibility approach [33,34].…”

“…By correcting the upper and lower bounds for each M hj andM hj and substituting Eqs. (33) and (34) into Model (32), transform it to a linear model as follows:…”