Solving LR-trapezoidal Fuzzy Linear Systems

Abstract

In this paper a new computational scheme is presented for fuzzy linear system ${\mathrm{A}}=\tilde{{\mathrm{b}}}$ where matrix A is a crisp one, and $\tilde{{\mathrm{x}}}$ and $\tilde{{\mathrm{b}}}$ are LR-trapezoidal fuzzy number vectors. By means of the basic operations of LR-trapezoidal fuzzy numbers, the original fuzzy equation is transformed into a crisp linear equation. Through solving the crisp linear equation, we find the solution of the LR-trapezoidal fuzzy linear equation. A directly sufficient condition for strong fuzzy solution is also investigated. An numerical example is put forth to show the method we constructed.