Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach

•All the variables are considered fuzzy, including input and output data and efficiency scores.•A lexicographic multi-objective linear programming optimization approach is proposed.•Fuzzy input and output targets are computed.•A super-efficiency fuzzy DEA model is also formulated to rank fuzzy effic...

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Bibliographic Details
Published in:Computers & industrial engineering Vol. 105; pp. 362 - 376
Main Authors: Hatami-Marbini, Adel, Ebrahimnejad, Ali, Lozano, Sebastián
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2017
Subjects:
Data envelopment analysis
Fuzzy mathematical programming
Fuzzy targets
Lexicographic multi-objective linear programming
Super-efficiency
Lexicographic multi-objective linear programming
Fuzzy targets
Fuzzy mathematical programming
Super-efficiency
Data envelopment analysis
ISSN:0360-8352
Online Access:Get full text
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Summary:•All the variables are considered fuzzy, including input and output data and efficiency scores.•A lexicographic multi-objective linear programming optimization approach is proposed.•Fuzzy input and output targets are computed.•A super-efficiency fuzzy DEA model is also formulated to rank fuzzy efficient DMUs. 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.
ISSN:0360-8352
DOI:10.1016/j.cie.2017.01.009