Design And Optimization Of Interval Type-2 Fuzzy System Based On Semi-tensor Product

Everything has a certain degree of uncertainty.In order to reduce the impact of uncertainty,scholars have proposed various control systems for handling uncertainty.Among them,the interval type-2 fuzzy system is considered a better approach.Compared with the traditional fuzzy system(type-1 fuzzy system),it has a stronger ability to handle uncertainty;compared with the type-2 fuzzy system,its concept and operation process are simpler.Although the interval type-2 fuzzy system is a simplified form of the type-2 fuzzy system,its logic operation process is still relatively complex.Therefore,this thesis employs the semi-tensor product of matrices theory to address this problem,thereby reducing the complexity of logical operations.The semi-tensor product of matrices is a mathematical tool for handling logical operations,which can transform the logical operations in fuzzy systems into algebraic operations,simplifying the complexity of fuzzy inference and providing a new perspective for analyzing and discussing interval type-2 fuzzy systems.The main results and innovation of this thesis are as follows:1.The semi-tensor product of matrices theory is extended,and an interval matrix semi-tensor product based on Boolean is proposed,which is called interval matrix semitensor product for short.The semi-tensor product of interval matrices not only allows Boolean multiplication operations on interval matrices of any dimension but also satisfies the associative and commutative laws.In addition,with the help of the identity matrix or the transposition interval matrix,the semi-tensor product of interval matrices can have pseudo-commutativity.2.The multivariable interval type-2 fuzzy systems are studied based on the semitensor product method.First,a mapping between interval type-2 fuzzy sets is defined,and the structural interval matrix of the mapping is given.Then,a multivariable interval type-2 fuzzy system is designed by the semi-tensor product of interval matrices method,and the mathematical expressions for each layer of the system are given.Finally,the validity of the designed system is verified by simulating the artificial pancreas system.3.The interval type-2 hierarchical fuzzy system is studied based on the semi-tensor product method.The decomposition technique of interval type-2 fuzzy relation matrix is proposed,which can decompose the original fuzzy relation matrix into two sub-fuzzy relation matrices.Based on the decomposition technique,the construction algorithms of series,parallel and hybrid interval type-2 hierarchical fuzzy systems are proposed.Then,the blood glucose controller of the artificial pancreas system is designed hierarchically to verify the effectiveness of the algorithm.4.The optimization strategy of interval type-2 fuzzy relation matrix is studied based on chaotic genetic algorithm.The basic concept,advantages and disadvantages of genetic algorithm are introduced.Aiming at the defects of genetic algorithm,chaotic mapping and chaotic disturbance are used to improve it.Based on the improved genetic algorithm,the optimization strategy of the interval type-2 fuzzy relation matrix is proposed.By optimizing interval type-2 fuzzy relation matrices of the blood glucose controller,the correctness of the designed optimization strategy is verified.