The General Solutions of Fuzzy Linear Matrix Equations

Abstract

The main aim of this paper is to illustrate and discuss consistent Fuzzy Linear Matrix Equations (shown as  $\mathbf{FLME}$) of the form $\sum ^{l}_{i=1}(A_{i}X_{i}B_{i})=C$for finding its fuzzy number solutions. Similar this equation is studied in \cite{m} based on Friedman's method \cite{k1}. Recently, Mikaeilvand et al.\cite{mn} proposed a novel method based on Ezzati's method \cite{e} for solving fuzzy linear systems, which numerically better than Friedman's method. In this article, we used this method for finding the general solutions of consistent FLME.The parametric form of fuzzy numbers is used. The embedding method is profited to transform fuzzy linear matrix equations to parametric linear equations, and a numerical procedure for calculating the solutions isdesigned.