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Differential Evolution Methods for the Fuzzy Extension of Functions

Author

Listed:
  • Luciano Stefanini

    () (Department of Economics, Università di Urbino "Carlo Bo")

Abstract

The paper illustrates a differential evolution (DE) algorithm to calculate the level-cuts of the fuzzy extension of a multidimensional real valued function to fuzzy numbers. The method decomposes the fuzzy extension engine into a set of "nested" min and max box-constrained op- timization problems and uses a form of the DE algorithm, based on multi populations which cooperate during the search phase and specialize, a part of the populations to find the the global min (corresponding to lower branch of the fuzzy extension) and a part of the populations to find the global max (corresponding to the upper branch), both gaining efficiency from the work done for a level-cut to the subsequent ones. A special ver- sion of the algorithm is designed to the case of differentiable functions, for which a representation of the fuzzy numbers is used to improve ef- ficiency and quality of calculations. The included computational results indicate that the DE method is a promising tool as its computational complexity grows on average superlinearly (of degree less than 1.5) in the number of variables of the function to be extended.

Suggested Citation

  • Luciano Stefanini, 2007. "Differential Evolution Methods for the Fuzzy Extension of Functions," Working Papers 0705, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2007.
  • Handle: RePEc:urb:wpaper:07_05
    as

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    File URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_07_05.pdf
    File Function: First version, 2007
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    References listed on IDEAS

    as
    1. Zmeskal, Zdenek, 2001. "Application of the fuzzy-stochastic methodology to appraising the firm value as a European call option," European Journal of Operational Research, Elsevier, vol. 135(2), pages 303-310, December.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Fuzzy Sets; Differential Evolution Method; Fuzzy Extension of Functions;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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