×

Fuzzy efficiency measures in data envelopment analysis. (English) Zbl 0965.90025

Summary: The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal with imprecise data, the notion of fuzziness has been introduced. This paper develops a procedure to measure the efficiencies of DMUs with fuzzy observations. The basic idea is to transform a fuzzy DEA model to a family of conventional crisp DEA models by applying the \(\alpha\)-cut approach. A pair of parametric programs is formulated to describe that family of crisp DEA models, via which the membership functions of the efficiency measures are derived. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for management. By extending to fuzzy environment, the DEA approach is made more powerful for applications.

MSC:

90B50 Management decision making, including multiple objectives
03E72 Theory of fuzzy sets, etc.
90C51 Interior-point methods
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Banker, R.D.; Charnes, A.; Cooper, W.W., Some models for estimating technical and scale efficiencies in data envelopment analysis, Management sci., 30, 1078-1092, (1984) · Zbl 0552.90055
[2] Bellman, R.E.; Zadeh, L.A., Decision-making in a fuzzy environment, Management sci., 17, B141-B164, (1970) · Zbl 0224.90032
[3] Buckley, J.J., Possibilistic linear programming with triangular fuzzy numbers, Fuzzy sets and systems, 26, 135-138, (1988) · Zbl 0644.90059
[4] Buckley, J.J., Solving possibilistic programming problems, Fuzzy sets and systems, 31, 329-341, (1989) · Zbl 0671.90049
[5] Charnes, A.; Cooper, W.W., The non-Archimedean CCR ratio for efficiency analysis: a rejoinder to Boyd and Färe, Eur. J. oper. res., 15, 333-334, (1984)
[6] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. oper. res., 2, 429-444, (1978) · Zbl 0416.90080
[7] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. oper. res., 3, 339, (1979) · Zbl 0425.90086
[8] Chen, S.H., Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy sets and systems, 17, 113-129, (1985) · Zbl 0618.90047
[9] Chen, C.B.; Klein, C.M., A simple approach to ranking a group of aggregated fuzzy utilities, IEEE trans. systems man cybernet. part B: cybernet., 27, 26-35, (1997)
[10] Cooper, W.W.; Thompson, R.G.; Thrall, R.M., Introduction: extensions and new developments in DEA, Ann. oper. res., 66, 3-45, (1996) · Zbl 0863.90003
[11] Ferguson, C.E.; Gould, J.P., ()
[12] Gal, T., Postoptimal analyses, Parametric programming, and related topics, (1979), McGraw-Hill New York
[13] Julien, B., An extension to possibilistic linear programming, Fuzzy sets and systems, 64, 195-206, (1994)
[14] Kao, C.; Li, C.C.; Chen, S.P., Parametric programming to the analysis of fuzzy queues, Fuzzy sets and systems, 107, 93-100, (1999) · Zbl 0947.90026
[15] Kaufmann, A., Introduction to the theory of fuzzy subsets, 1, (1975), Academic Press New York · Zbl 0332.02063
[16] Lai, Y.J.; Hwang, C.L., A new approach to some possibilistic linear programming problems, Fuzzy sets and systems, 49, 121-133, (1992)
[17] Liou, T.S.; Wang, M.J., Ranking fuzzy numbers with integral values, Fuzzy sets and systems, 49, 247-255, (1992) · Zbl 1229.03043
[18] Luhandjula, M.K., Linear programming with a possibilistic objective function, Eur. J. oper. res., 31, 110-117, (1987) · Zbl 0635.90057
[19] Rommelfanger, H.; Wolf, J.; Hanuscheck, R., Linear programming with fuzzy objectives, Fuzzy sets and systems, 29, 31-48, (1989) · Zbl 0662.90045
[20] Seiford, L.M., Data envelopment analysis: the evolution of the state of the art (1978-1995), J. productivity anal., 7, 99-137, (1996)
[21] Sengupta, L.M., Data envelopment analysis for efficiency measurement in the stochastic case, Comput. oper. res., 14, 117-129, (1987) · Zbl 0617.90051
[22] Sengupta, L.M., Robust efficiency measures in a stochastic efficiency model, Internat. J. systems sci., 19, 779-791, (1988) · Zbl 0647.90012
[23] Sengupta, L.M., Measuring economic efficiency with stochastic input—output data, Internat. J. systems sci., 20, 203-213, (1989) · Zbl 0671.90001
[24] Sengupta, L.M., A fuzzy system approach in data envelopment analysis, Comput. math. appl., 24, 259-266, (1992) · Zbl 0765.90004
[25] Sengupta, L.M., Non-parametric approach to stochastic programming, Internat. J. systems sci., 24, 857-871, (1993) · Zbl 0777.90037
[26] Tanaka, H.; Ichihashi, H.; Asai, K., A formulation of fuzzy linear programming problem based on comparison of fuzzy number, Control and cybernet., 13, 185-194, (1984) · Zbl 0551.90062
[27] Tseng, T.Y.; Klein, C.M., New algorithm for the ranking procedure in fuzzy decision making, IEEE trans. systems man cybernet., 19, 1289-1296, (1989)
[28] Yager, R.R., A characterization of the extension principle, Fuzzy sets and systems, 18, 205-217, (1986) · Zbl 0628.04005
[29] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. systems man cybernet. SMC-1, 28-44, (1973) · Zbl 0273.93002
[30] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
[31] Zimmermann, H.J., ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.