Approximate Solutions Of Two Classes Of Linear Systems Based On LR-trapezoidal Fuzzy Numbers

The parameters of some linear systems always have some or all uncertainties,which can be expressed and calculated by fuzzy numbers.Fuzzy linear system equations are widely used in many practical problems in physics,mechanics,economics,modern engineering technology and other scientific fields.It is particularly important to solve the numerical solution of fuzzy linear system.Therefore,linear systems related to fuzzy numbers and their applications have attracted the attention of many scholars in recent decades,and new theories and methods emerge one after another.In this paper,we study the solutions of general LR-trapezoidal fuzzy linear systems and LR-trapezoidal dual fuzzy linear systems using a complete matrix method.Based on the IR-trapezoidal fuzzy matrix and its basic operation,the calculation method of Sylvester equation AX+XB=F is discussed by direct product.First,the extended model of the original fuzzy matrix equation is established,then the solvability of the model is analyzed,and the specific calculation formula of the model is given.Then,the existence condition of the strong fuzzy solution is defined and studied,and a new method for solving the linear matrix system based on LR trapezoidal fuzzy number is explored.Numerical examples show that our method is effective and feasible,which greatly simplifies the calculation.Since trapezoidal fuzzy numbers are extensions of triangular fuzzy numbers,our work enriches and develops the theory of fuzzy linear systems.