General strong fuzzy solutions of fuzzy Sylvester matrix equations involving the BT inverse

Abstract

This paper aims to solve the fuzzy Sylvester matrix equation (FSME) AX˜+X˜B=C˜, in which A, B are n×n and m×m crisp matrices, and C˜ is a n×m fuzzy matrix. Using the Kronecker product, we transform the FSME into an mn×mn fuzzy linear system. Firstly, we obtain the necessary and sufficient conditions for the existence of strong fuzzy solutions to the FSME by using the BT inverse of the coefficient matrix. Secondly, we investigate the existence of a nonnegative BT inverse by using its block structure. Next, we derive general strong fuzzy solutions to a class of FSME and establish an algorithm to obtain general strong fuzzy solutions to the FSME by the BT inverse. Finally, we give three numerical examples and an applied example in the economy to illustrate the proposed methods.