Solving fuzzy linear systems using a block representation of generalized inverses: The Moore-Penrose inverse

In this paper we present a new method for solving an m×n fuzzy linear system (FLS), AX˜=Y˜, where the coefficient matrix A is real, using the block representation of generalized inverses. A necessary and sufficient condition for a block matrix to be the Moore-Penrose inverse of the full rank matrix associated to a FLS is given. We obtain a necessary and sufficient condition for the existence of solutions of a FLS, with arbitrary real coefficient matrix. The exact algebraic form, with respect to the Moore-Penrose inverse, of any solution of FLS of this type is established. A general, efficient and universal method for obtaining the exact solutions is introduced. Some numerical examples are presented to illustrate the proposed method.