TY - JOUR
T1 - Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach
AU - Hatami-Marbini, Adel
AU - Ebrahimnejad, Ali
AU - Lozano, Sebastián
N1 - Publisher Copyright:
© 2017 Elsevier Ltd
PY - 2017/3/1
Y1 - 2017/3/1
N2 - There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature.
AB - There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature.
KW - Data envelopment analysis
KW - Fuzzy mathematical programming
KW - Fuzzy targets
KW - Lexicographic multi-objective linear programming
KW - Super-efficiency
UR - http://www.scopus.com/inward/record.url?scp=85010953270&partnerID=8YFLogxK
U2 - 10.1016/j.cie.2017.01.009
DO - 10.1016/j.cie.2017.01.009
M3 - Article
AN - SCOPUS:85010953270
VL - 105
SP - 362
EP - 376
JO - Computers and Industrial Engineering
JF - Computers and Industrial Engineering
SN - 0360-8352
ER -