Construction and optimization of fuzzy relation matrices model based-on semi-tensor product

On base of semi-tensor product (STP) of matrices, this paper proposes a new and more general framework to construct a matrix-based fuzzy relation structure model for multi-input multi-output (MIMO) fuzzy control systems. The measured sampling data of inputs and outputs are assumed to be obtained from experiments. Instead of building the fuzzy logical rule sets of a fuzzy dynamical controller, the whole designing process is realized via matrix expression and algebraic algorithms. After the input and output data pairs which satisfy a fuzzy dynamic process are described by vectors, the fuzzy relation matrixes of all input and output variables for each data pair are calculated respectively so its fuzzy relation matrix can be got. Final fuzzy relation matrix of all measured data can be achieved by fuzzy disjunction operation and then optimized by the fuzzy α-interception matrix. The new technique gives one general design method to obtain fuzzy relation matrix expression of multiple variables fuzzy control systems. It is particularly suitable to design non-decomposable multi-output fuzzy controllers, which is not solvable directly by the traditional decomposed control design methods.