A straightforward approach for solving dual fuzzy linear systems

Abstract

The main purpose of this paper is to solve a dual fuzzy linear system algebraically. In considered systems, the coefficient matrices are crisp-valued matrices and the left and right hand sides vectors are fuzzy number-valued vectors. Two types of solutions are defined and the relationship between them is investigated. Finally, based on the obtained results, a simple method is presented to obtain a unique algebraic solution of a dual fuzzy linear system. The main advantage of the proposed method over existing methods is that it does not need to convert a dual fuzzy linear system to two crisp linear systems. Also, a new necessary and sufficient condition for the existence of unique algebraic solution of a dual fuzzy linear system is presented. To illustrate our method, two numerical examples and an applied example in economy are given.