Solving fuzzy linear systems by a block representation of generalized inverse: the core inverse

Abstract

This paper presents a method for solving fuzzy linear systems, where the coefficient matrix is an $$n\times n$$ real matrix, using a block structure of the Core inverse, and we use the Hartwig–Spindelbock decomposition to obtain the Core inverse of the coefficient matrix A. The aim of this paper is twofold. First, we obtain a strong fuzzy solution of fuzzy linear systems, and a necessary and sufficient condition for the existence strong fuzzy solution of fuzzy linear systems are derived using the Core inverse of the coefficient matrix A. Second, general strong fuzzy solutions of fuzzy linear systems are derived, and an algorithm for obtaining general strong fuzzy solutions of fuzzy linear systems by Core inverse is also established. Finally, some examples are given to illustrate the validity of the proposed method.