Abstract
In this paper systems of linear equations Ax = b, where both A and b contain 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.
This work is supported by the grant no. N519 020 31/3900 from the Polish Ministry of Science and Higher Education (Fund for Scientific Research in 2006-2007).
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Viet, N.H., Kleiber, M. (2007). An Evolutionary Approach for Approximating the Solutions of Systems of Linear Fuzzy Equations. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71618-1_63
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DOI: https://doi.org/10.1007/978-3-540-71618-1_63
Publisher Name: Springer, Berlin, Heidelberg
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