The Solution Of Fuzzy Linear System Based On LR-Trapezoidal Fuzzy Numbers And Its Numerical Calculation

Fuzzy linear system is widely used in engineering analysis,automatic control and economic finance fields.In fact,in the discussion of many nonlinear system problems,the first consideration is whether it can be converted into a linear prob-lem in a certain sense in concrete mathematical modelling and solution.However,uncertainty of parameters is often involved in the specific process.So there has already a lot of research on fuzzy linear system.But the solution of fuzzy linear system strictly limits the universality of its application and loses a lot of useful information to a large extent.Moreover,the present research has not considered the fuzzy linear system with LR-trapezoidal fuzzy numbers and dual fuzzy linear system with LR-trapezoidal fuzzy numbers.Based on the these considerations,this article systematically studies the solving methods of fuzzy linear system and dual fuzzy linear system based on LR-trapezoidal fuzzy numbers on the basis of extending LR-trapezoidal fuzzy numbers.Firstly,using the structure characteristics of LR-trapezoidal fuzzy numbers,the fuzzy linear system could be transformed into distinct linear matrix system in which the parameter r(r ?[0,1])be not contained,the strong fuzzy solutions and weak fuzzy solutions of fuzzy linear system are discussed by using the generalized inverse of the coefficient matrix,and their iterative methods of the numerical calculation are discussed.Secondly,using the addition and multiplication of LR-trapezoidal fuzzy num-bers,the 1-cutting system of the dual fuzzy linear system construct the center of fuzzy solution and the optimization problem solve the extension of fuzzy solution,thus the exact or approximate fuzzy solutions are obtained.Finally,numerical examples of the fuzzy linear system and dual fuzzy linear system based on LR-trapezoidal fuzzy numbers are given.