Solutions of Fuzzy Linear Systems

Abstract

In this paper, we investigate the solution of system of fuzzy linear equations, Ax  b , where A is a crisp real n  n matrix and
b is a vector consisting of n triangular fuzzy numbers. Assuming that the unknown vector x is a fuzzy number vector of the same
type as b , and defining the addition and scalar-multiplication by Zadeh’s extension principle, we propose a method of solution that
replaces the n  n fuzzy system by a 3n  3n crisp linear system MX  B , where M is a block symmetric matrix
depending on A and B is a vector whose components are rearranged parameters of the fuzzy numbers in b . We provide
conditions for the existence of a unique fuzzy solution of the system under investigation. We use the Mathematica package for
symbolic and numeric computation.