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Fuzzy Dual Programming

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 359))

Abstract

To tackle optimization problems with uncertain parameters and variables, this chapter considers the use of fuzzy dual numbers, vectors and matrices.

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References

  • Ben-Tal A., El Ghaoui, L. and Nemirovski, A. (2009). Robust Optimization. Princeton Series in Applied Mathematics, Princeton University Press.

    Google Scholar 

  • Delgado M., J.L. Verdegay and M.A. Vila (1987). Imprecise costs in mathematical programming problems, Control and Cybernetics, vol. 16, pp. 114–121.

    Google Scholar 

  • Gal T. and H.J. Greenbers (eds) (1997). Advances in sensitivity analysis and parametric programming, Kluwer Academic Publishers.

    Google Scholar 

  • Kosinsky W., (2006). On Fuzzy Number Calculus, International Journal of Applied Mathematics and Computer Science, vol. 16, No. 1, pp. 51–57.

    Google Scholar 

  • Nasseri H., (2006). Fuzzy Numbers: Positive and Nonnegative, International Mathematical Forum, vol. 3, pp. 1777–1780.

    Google Scholar 

  • Ruszczynski A. and A. Shapiro (2003). Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10, Elsevier.

    Google Scholar 

  • Tanaka, H., Ichihashi, H., Asai, K. (1974). On fuzzy mathematical programming, J. Cybernet. 3, pp. 37–46.

    Google Scholar 

  • H. J. Zimmermann (1986). Fuzzy Sets Theory and Mathematical Programming, in A. Jones et al. (eds.), Fuzzy Sets Theory and Applications, D. Reidel Publishing Company, pp. 99–114.

    Google Scholar 

  • R. Bellman, Dynamic Programming, First Princeton Landmarks in Mathematics ed., Princeton University Press, Princeton, 2010.

    Google Scholar 

  • R. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, 1970, Management Science 17B, pp. 141–164.

    Google Scholar 

  • O. Esogbue and R. Bellman, Fuzzy dynamic programming and its extensions, TIMS/Studies in the Management Sciences, 20, pp. 147–167.

    Google Scholar 

  • J. Kacprzyk, Multistage decision making under fuzziness, Verlag TÜV, Rheinland, Cologne, 1983.

    Google Scholar 

  • P. K. Parida, Fuzzy dynamic system approach to multistage decision making problems, Ultra Scientist, vol. 25(2)A, pp. 350–360, 2013.

    Google Scholar 

  • J. Kacprzyk and A. O. Esogbue, Fuzzy dynamic programming: Main developments and applications, Fuzzy sets and systems 81 (1996). pp. 31–45.

    Google Scholar 

  • R. M. Faye, S. Sawadogo and F. Mora-Camino, Logique floue appliquée à la gestion à long-terme des resources en eau, Revue des sciences de l’eau, vol. 15, no. 3, 2002, pp. 579–596.

    Google Scholar 

  • E. M. Capitanul, C. A. N. Cosenza, W. El Moudani and F. Mora-Camino, Airport Investment Risk Assessment under Uncertainty, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, World Academy of Science, Engineering and Technology (WASET), 2014, 8 (9), pp. 1202–1206.

    Google Scholar 

  • E. M. Capitanul, Airport strategic planning under uncertainty: Fuzzy dual dynamic programming approach, PhD Thesis, Toulouse University-ENAC, Sept. 2016.

    Google Scholar 

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Correspondence to Felix Mora-Camino .

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Mora-Camino, F., Nunes Cosenza, C.A. (2018). Fuzzy Dual Programming. In: Fuzzy Dual Numbers. Studies in Fuzziness and Soft Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-65418-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-65418-8_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65417-1

  • Online ISBN: 978-3-319-65418-8

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