An Evolutionary Approach for Approximating the Solutions of Systems of Linear Fuzzy Equations

Authors:
Nguyen Hoang Viet;Michał Kleiber
Affiliations:
Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland;Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland
Venue:
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Year:
2007

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Abstract

In this paper systems of linear equations Ax= b, where both Aand bcontain uncertain factors in terms of fuzziness are investigated. The classical solutions being vectors of fuzzy numbers are considered. The complex problem of finding the exact classical solutions is replaced by a corresponding optimization task with the cost function based on the Hausdorff metric. This cost function is next minimized with use of genetic algorithms. A number of numerical experiments are provided in order to verify the given approach. The results and some conclusions are also included.