A Genetic Algorithm Approach for Solving Fuzzy Linear and Quadratic Equations

Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076948

References:

[1] J.J. Buckley, Y. Qu, Solving fuzzy equations: a new solution concept, Fuzzy Sets and Systems 39 (1991) 291-301.
[2] S. Abbasbandy and B. Asady, "Newton-s method for solving fuzzy nonlinear equations", Applied Mathematics and Computation, Vol. 159, pp. 349-356, 2004.
[3] J.J. Buckley and E. Eslami, "Neural net solutions to fuzzy problems: the quadratic equation", Fuzzy Sets and Systems, Vol. 86, pp. 289-298, 1997.
[4] S. Abbasbandy and M. Otadi, "Numerical solution of fuzzy polynomials by fuzzy neural network", Applied Mathematics and Computation, Vol. 181, pp. 1084-1089, 2006.
[5] J.J. Buckley and E. Eslami, "Solving Fuzzy Equations Using Monte Carlo Methods", Proceedings of Asian Fuzzy System Society International Conference, September 17- 20, China, pp-133-135, 2006.
[6] Hassan Mishmast Nehi, "Fuzzy linear programming, single and multiobjective functions", Ph.D of Mathematics Thesis, University of Kerman, 2003.
[7] R. A. Aliev, B. Fazlollahi, and R. M. Vahidov, "Genetic algorithm-based learning of fuzzy neural network, Part 1: feed-forward fuzzy neural networks", Fuzzy Sets and Systems, Vol. 118, No. 2, pp. 351-358, 2001.