Abstract
While the traditional data envelopment analysis (DEA) requires precise input and output data, available data is usually imprecise and vague. “Fuzzy DEA” integrates the concept of fuzzy set theory with the traditional DEA by representing imprecise and vague data with fuzzy sets. In this paper, a credibility approach is proposed as a way to solve the fuzzy DEA model. The approach transforms a fuzzy DEA model into a well-defined credibility programming model, in which fuzzy variables are replaced by “expected credits” in terms of credibility measures. It is shown that when the membership functions of fuzzy data are trapezoidal, the credibility programming model becomes a linear programming model. Numerical examples are given to illustrate the proposed approach and results are compared with those obtained with alternative approaches.
This research was supported, in part, by the National Textile Center of the United States of America (Grant Number: I01-S01).
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References
Arnade, C. A. (1994): Using data envelopment analysis to measure international agricultural efficiency and productivity, United States Department of Agriculture, Economic Research Service, Technical Bulletin, 1831, 1–30.
Banker, R. D., Charnes, A. and Cooper, W. W. (1984) Some models for estimating technical and scale inefficiency in data envelopment analysis, Management Science, 30, 1078–1092.
Banker, R. D., Chang, H. and Cooper, W. W. (1996) Simulation studies of efficiency, returns to scale and misspecification with nonlinear functions in DEA, Annals of Operations Research, 66, 233–253.
Charnes, A., Cooper, W. W., Golany, B. and Seiford. L. M. (1985) Foundation of data envelopment analysis for Pareto-Koopmans efficient empirical production functions, Journal of Econometrics, 30, 91–107.
Charnes, A., Cooper, W. W., Lewin, A. Y. and Seiford, L. M. (1994) Data Envelopment Analysis: Theory, Methodology, and Application, Kluwer Academic Publishers, London.
Cooper, W. W., Seiford, L. M. and Tone, K. (2000) Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Kluwer Academic Publishers, London.
Charnes, A., Cooper, W. W. and Rhodes, E. (1978) Measuring the efficiency of decision-making units, European Journal of Operational Research, 2, 429–444.
Dubois, D. and Prade, H. (1988) Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, New York.
Fang, S. -C. and Puthenpura, S. (1993) Linear Optimization and Extensions: Theory and Algorithms, Prentice Hall, Englewood Cliffs, New Jersey.
Guo, P. and Tanaka, H. (2001) Fuzzy DEA: A perceptual evaluation method, Fuzzy Sets and Systems, 119, 149–160.
Kahraman, C. and Tolga, E. (1998) Data envelopment analysis using fuzzy concept, Proceedings of the 28th International Symposium on Multiple-Valued Logic, 338–343.
Kao, C. and Liu, S. -T. (2000) Fuzzy efficiency measures in data envelopment analysis, Fuzzy Sets and Systems, 113, 427–437.
Lertworasirikul, S. (2001) Fuzzy Data Envelopment Analysis for Supply Chain Modeling and Analysis, Dissertation Proposal in Industrial Engineering, North Carolina State University.
Lertworasirikul, S., Fang, S.-C., Joines, J. A. and Nuttle, H. L. W. (2001) Fuzzy data envelopment analysis (DEA): A possibility approach, submitted to Fuzzy Sets and Systems.
Lertworasirikul, S., Fang, S.-C., Joines, J. A. and Nuttle, H. L. W. (2002) A possibility approach to fuzzy data envelopment analysis, to appear in the Proceedings of 8th International Conference on Fuzzy Theory and Technology.
Liu, B. (2002) Toward fuzzy optimization without mathematical ambiguity, to appear in Fuzzy Optimization and Decision Making, 1–1.
Liu, B. (2001a) Uncertain programming: A unifying optimization theory in various uncertain environments, Applied Mathematics and Computation, 120, 227–234.
Meada, Y., Entani, T. and Tanaka, H. (1998) Fuzzy DEA with interval efficiency, Proceedings of the 6th European Congress on Intelligent Techniques and Soft Computing, 2, 1067–1071.
Seiford, L. M. and Thrall, R. M. (1990) Recent development in DEA: The mathematical programming approach to frontier analysis, Journal of Econometrics, 46, 7–38.
Sengupta, J. K. (1992) A fuzzy systems approach in data envelopment analysis, Computers and Mathematics with Applications, 24, 259–266.
Sengupta, J. K. (1995) Dynamics of Data Envelopment Analysis: Theory of Systems Efficiency, Kluwer Academic Publishers, London.
Zadeh, L. A. (1965) Fuzzy sets, Information and Control 8, 338–353.
Zadeh, L. A. (1978) Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3–28.
Zimmermann, H. J. (1996) Fuzzy Set Theory and Its Application, Kluwer Academic Publishers, London.
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Lertworasirikul, S., Fang, SC., Joines, J.A., Nuttle, H.L.W. (2003). Fuzzy Data Envelopment Analysis: A Credibility Approach. In: Verdegay, JL. (eds) Fuzzy Sets Based Heuristics for Optimization. Studies in Fuzziness and Soft Computing, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36461-0_10
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DOI: https://doi.org/10.1007/978-3-540-36461-0_10
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