Abstract
This paper analyzes a linear system of equations when the right- hand side is a fuzzy vector and the coecient matrix is a crisp M-matrix. The fuzzy linear system (FLS) is converted to the equivalent crisp system with coecient matrix of dimension 2 n ◊ 2n. However, solving this crisp system is dicult for large n because of dimensionality problems . It is shown that this diculty may be avoided by computing the inverse of an n◊n matrix instead of Z 1 . matrix in a fuzzy linear system is an M-matrix. We first study the properties of this system and then propose a solution using the Schur complement. Section 2 provides preliminaries for fuzzy numbers and fuzzy linear systems. Several M-matrix properties and the Schur complement formula are also stated. The relationship between an M-matrix and its crisp matrix and the existence and expression of the solution to the fuzzy linear system using the Schur complement are discussed in section 3. Numerical examples to illustrate previous sections are given in Section 4. 2. Preliminaries 2.1. Fuzzy Numbers and Fuzzy Linear Systems. In this section we recall the basic notion of fuzzy numbers arithmetic and fuzzy linear system.
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