Complex Fuzzy Sylvester Matrix Equation Calculation Method

Many linear systems have some or all parameters of uncertainty,which can be expressed and calculated by means of fuzzy numbers.in the past two decades,the study of uncertain linear systems based on some elements of fuzzy numbers and their applications have attracted the attention of many scholars at home and abroad,and new theories and methods have emerged one after another.In view of the above facts and the wide application of linear matrix equation,this paper discusses the calculation method of the Sylvester matrix equation AX+XB=C with complex fuzzy number representing uncertain element,where C is a complex fuzzy matrix and X is an unknown complex fuzzy vector.A is a real matrix of order m ×m and B is a real matrix of order n x n,by using matrix theory and method,two kinds of matrix are constructed to solve the fuzzy Sylvester matrix equation,by using complex fuzzy matrix equation is extended to clear matrix equation,we obtained the general complex fuzzy approximation solution of matrix equation,for LR complex fuzzy matrix through the Kronecker product complex fuzzy linear system is transformed into equivalent high-order fuzzy linear systems and fuzzy approximate solution is obtained.the structure of this paper is:firstly,this paper introduces the definition and operation of fuzzy number,and generalized inverse matrix and the basic concepts such as Kronecker product.secondly,the complex fuzzy Sylvester matrix equation is proposed on the basis of solving the positive fully fuzzy matrix equation,and its calculation model and formula are constructed.the conditions of the solution are analyzed.and finally,numerical example is given to illustrate the feasibility of the structure method.