| When some parameters in linear system and nonlinear system are fuzzy numbers, these systems are called fuzzy linear system and fuzzy nonlinear system, respectively. These systems come from many subject fields, such as mathematics, physics, statistics,cybernetics and so on. Generally, to obtain an analytical solution of these systems is a difficult thing. Therefore, how to find their numerical solution is an important interesting work and this is just what we study in the paper.In Chapter 2, a class of fuzzy linear system is translated into an equivalent unconstrained minimization problem, and a conjugate gradient algorithm is applied to solve the equivalent problem. The numerical optimization solution is just the numerical solution of the fuzzy linear system. Numerical results show that the algorithm is always valid whether the system matrix is symmetric or not, and its iterative numbers are less than ones gotten by using the existent steepest descent algorithm [3].In Chapter 3, the definitions of a class of overdetermined fuzzy linear system and its least square solution are given. Furthermore, the new system is translated into an equivalent uncon-strained optimization problem. Some properties on the solution of the system are discussed. And then, a conjugate gradient algorithm is proposed for solving the solution of the system. Numerical results show that the algorithm is so valid that the exact least square solution of the system is gotten after only finite iterations.In Chapter 4, the parameter form of a class of fuzzy nonlinear system is translated into an equivalent unconstrained optimization problem. A hybrid conjugate gradient is applied to solve the corresponding optimization problem. The numerical optimization solution is just the numerical solution of the fuzzy nonlinear system. Numerical results show that the algorithm is valid and its iterative numbers are less than ones gotten by using the existent steepest descent algorithm [2].
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