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Positive and normative use of fuzzy DEA‐BCC models: A critical view on NATO enlargement
Author(s) -
HatamiMarbini Adel,
Tavana Madjid,
Saati Saber,
Agrell Per J.
Publication year - 2013
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2012.00871.x
Subject(s) - data envelopment analysis , fuzzy logic , variable (mathematics) , interval (graph theory) , mathematical optimization , fuzzy set , computer science , value (mathematics) , linear programming , set (abstract data type) , mathematics , artificial intelligence , machine learning , mathematical analysis , combinatorics , programming language
Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the input and output of a set of comparable decision‐making units (DMUs) by evaluating their relative efficiency. The traditional DEA methods require accurate measurement of both the inputs and outputs. However, the real evaluation of the DMUs is often characterized by imprecision and uncertainty in data definitions and measurements. The development of fuzzy DEA (FDEA) with imprecise and ambiguous data has extended the scope of application for efficiency measurement. The purpose of this paper is to develop a fuzzy DEA framework with a BCC model for measuring crisp and interval efficiencies in fuzzy environments. We use an α‐level approach to convert the fuzzy Banker, Charnes, and Cooper (BCC) (variable returns to scale) model into an interval programming model. Instead of comparing the equality (or inequality) of the two intervals, we define a variable in the interval to satisfy our constraints and maximize the efficiency value. We present a numerical example to show the similarities and differences between our solution and the solutions obtained from four fuzzy DEA methods in the literature. In addition, a case study for NATO enlargement is presented to illustrate the applicability of the proposed method.