Numerical Solutions And Applications In Control And Economics Of Two Fuzzy Linear Systems

There are a lot of imprecise phenomena in the real world.Besides probability,fuzzy mathematics is the other method to describe imprecise phenomena.Fuzzy mathematics has many applications in engineering,control theory,image recognition,artificial intelligence,economy and finance.Sylvester-like matrix equation is a general form of Sylvester matrix equation,generalized Sylvester matrix equation and T-Sylvester matrix equation,these equations are used widely in the design of control system,signal processing,image restoration,partial differential equation and large-scale linear dynamic system.The input-output model is an important tool in national economic accounting,resource allocation and other economic research.Since the data in applications is imprecise,the two linear systems with fuzzy numbers coefficients are discussed in this thesis.For fuzzy Sylvester-like matrix equation,the function in the equation is assumed to be linear operator of fuzzy matrix,the equation can be transformed into 2n × 2m matrix equation by using extension method,and simplified further by using permutation matrices.Finally,the fuzzy problem is transformed to two Sylvester-like matrix equations with crisp coefficients.For the existence of fuzzy solution,the two transformed equations can be analyzed by using related theory of linear equations.In the topic of input-output model,fuzzy static input-output model and fuzzy dynamic input-output model are studied in this thesis.Using a pair of functions to express fuzzy number,the original problem is converted to crisp linear equations by using ?-cut and fuzzy number operation.According to the background of the model in macroeconomics,the conditions for the existence of fuzzy positive solutions are discussed.Here,numerical algorithms are also developed based on the transformed equations to solve them,our methods can reduce the calculation amount effectively.Eventually,the correctness and effectiveness of numerical algorithms in this thesis are verified by large scale numerical examples and numerical simulations with data in China Statistical Yearbook respectively.