Abstract
In this paper we propose a method for solving Data Envelopment Analysis (DEA) problems involving uncertainty generated by the opinion of multiple experts. Experts opinions define the values of inputs and outputs, and they are handled with interval Type-2 fuzzy sets. The proposed method is an extension of the classic CCR model, solved using a centroid-based strategy to reduce computations.
Juan Carlos Figueroa-García is Assistant Professor at the Universidad Distrital Francisco José de Caldas, Bogotá - Colombia.
Carlos Eduardo Castro-Cabrera is undergraduate student of the Industrial Engineering Dept. of the Universidad Distrital Francisco José de Caldas, Bogotá - Colombia
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Charnes, A., Cooper, W., Rhones, E.: Measuring the efficiency of decision making units. Eur. J. Oper. Res. 6, 429–444 (1978)
Sengupta, J.: A fuzzy systems approach in data envelopment analysis. Comput. Math. Appl. 24(8–9), 259–266 (1992)
Kahraman, C., Tolga, E.: Data envelopment analysis using fuzzy concept. In: 28th IEEE International Symposium on Multiple-Valued Logic, pp. 338–342. IEEE (1998)
Triantis, K., Girod, O.: A mathematical programming approach for measuring technical efficiency in a fuzzy environment. J. Prod. Anal. 10(1), 85–102 (1998)
Girod, O., Triantis, E.K.: The evaluation of productive efficiency using a fuzzy mathematical programming approach: the case of the newspaper preprint insertion process. IEEE Trans. Eng. Manage. 46(4), 429–443 (1999)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice Hall, Englewood cliffs (2001)
Mendel, J.M., Wu, D.: Perceptual Computing: Aiding People in Making Subjective Judgments. Wiley, Hoboken (2010)
Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel algorithms for Interval Type-2 fuzzy sets and systems. In: Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 26, pp. 184–189. IEEE (2007)
Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel Algorithms. IEEE Trans. Fuzzy Syst. 17(4), 923–934 (2009)
Mendel, J.M., Liu, F.: Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set. IEEE Trans. Fuzzy Syst. 15(2), 309–320 (2007)
Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132(1), 195–220 (2001)
Celemin, C., Melgarejo, M.: A proposal to speed up the computation of the centroid of an interval Type-2 fuzzy set. Adv. Fuzzy Syst 2013, 17 (2013). (Article ID 158969)
Melgarejo, M., Bernal, K.: A fast recursive method to compute the generalized centroid of an interval type-2 fuzzy set. In: Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 26, pp. 190–194. IEEE (2007)
Lertworasirikul, S., Fang, S.C., Joines, J.A., Nuttle, H.L.: Fuzzy data envelopment analysis (DEA): a possibility approach. Fuzzy Sets Syst. 139(2), 379–394 (2003)
Lertworasirikul, S., Fang, S.C., Joines, J.A., Nuttle, H.L.: A possibility approach to fuzzy data envelopment analysis. In: 6th Joint Conference on Information Science, pp. 176–179 (2002)
Karsak, E.: Using data envelopment analysis for evaluating flexible manufacturing systems in the presence of imprecise data. Int. J. Adv. Manuf. Technol. 35(9–10), 867–874 (2008)
Girod, O., Triantis E,K.: Measuring technical efficiency in a fuzzy environment. Ph.D. dissertation, Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University (1996)
Hatami-Marbini, A., Emrouznejad, A., Tavana, M.: A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur. J. Oper. Res. 214(3), 457–472 (2011)
Cooper, W., Lawrence, M.S., Kaouru, T.: Introduction to Data Envelopment Analysis and Its Uses. Springer-Verlag, Heidelberg (2006)
Figueroa-García J.C. A general model for linear programming with interval type-2 fuzzy technological coefficients. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1–6. IEEE (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Figueroa-García, J.C., Castro-Cabrera, C.E. (2015). On Solving CCR-DEA Problems Involving Type-2 Fuzzy Uncertainty Using Centroid-Based Optimization. In: Huang, DS., Han, K. (eds) Advanced Intelligent Computing Theories and Applications. ICIC 2015. Lecture Notes in Computer Science(), vol 9227. Springer, Cham. https://doi.org/10.1007/978-3-319-22053-6_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-22053-6_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22052-9
Online ISBN: 978-3-319-22053-6
eBook Packages: Computer ScienceComputer Science (R0)