{"title":"A Genetic Algorithm Approach for Solving Fuzzy Linear and Quadratic Equations ","authors":"M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin","volume":4,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":215,"pagesEnd":220,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11254","abstract":"

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx\u0303=B\u0303 and Ãx\u03032<\/sup> + B\u0303x\u0303=C\u0303 , where Ã, B\u0303, C\u0303 and x\u0303 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 x\u0303b<\/sub> . In this proposed method the final reached x\u0303b<\/sub> is not only restricted to fuzzy triangular and it can be fuzzy number.<\/p>\r\n","references":" J.J. Buckley, Y. Qu, Solving fuzzy equations: a new solution concept,\r\nFuzzy Sets and Systems 39 (1991) 291-301.\r\n S. Abbasbandy and B. Asady, \"Newton-s method for solving fuzzy\r\nnonlinear equations\", Applied Mathematics and Computation, Vol. 159,\r\npp. 349-356, 2004.\r\n J.J. Buckley and E. Eslami, \"Neural net solutions to fuzzy problems: the\r\nquadratic equation\", Fuzzy Sets and Systems, Vol. 86, pp. 289-298,\r\n1997.\r\n S. Abbasbandy and M. Otadi, \"Numerical solution of fuzzy polynomials\r\nby fuzzy neural network\", Applied Mathematics and Computation, Vol.\r\n181, pp. 1084-1089, 2006.\r\n J.J. Buckley and E. Eslami, \"Solving Fuzzy Equations Using Monte\r\nCarlo Methods\", Proceedings of Asian Fuzzy System Society\r\nInternational Conference, September 17- 20, China, pp-133-135, 2006.\r\n Hassan Mishmast Nehi, \"Fuzzy linear programming, single and\r\nmultiobjective functions\", Ph.D of Mathematics Thesis, University of\r\nKerman, 2003.\r\n R. A. Aliev, B. Fazlollahi, and R. M. Vahidov, \"Genetic algorithm-based\r\nlearning of fuzzy neural network, Part 1: feed-forward fuzzy neural\r\nnetworks\", Fuzzy Sets and Systems, Vol. 118, No. 2, pp. 351-358, 2001.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 4, 2007"}