Differential Evolution Methods for the Fuzzy Extension of Functions

Luciano Stefanini ()

No 705, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

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.

Keywords: Fuzzy Sets; Differential Evolution Method; Fuzzy Extension of Functions (search for similar items in EconPapers)
JEL-codes: C00 C60 C63 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2007, Revised 2007
New Economics Papers: this item is included in nep-cmp
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