Solving A Class Of Fuzzy Systems And Their Applications

In view of the difficulties of computation and weak applicability of the methods to solve the traditional fuzzy linear system and quadratic fuzzy system of equations. By the homeomorphic property between the bounded fuzzy numbers and the same ordinal bounded monotone functions on[-1,1], the fuzzy systems are equivalently transformed into the polynomial systems. The fuzzy structured theory is introduced with the traditional Gaussian elimination method, QR decomposition method, quasi-Newton method, a complete and effective method is set up to solve the fuzzy systems.Compared with the traditional method, solving the fuzzy systems by the method proposed in this paper makes the application scope expanded as well as simplifies the difficult expression of fuzzy numbers and complicated computation, and give the necessary and sufficient condition of a fuzzy solution existence for the general fuzzy linear system, the fully fuzzy system and the quadratic fuzzy system of equations.For the solution of the general fuzzy linear system, the fully fuzzy linear system and the quadratic fuzzy system of equations, three examples of applications which are the model of film vibration in the physical field, the model of supply-demand relationship in the economic field and the model of three sink in the engineering field provide the basis for the practical application solving the fuzzy systems.