General strong fuzzy solutions of complex fuzzy matrix equations involving the Moore-Penrose weak group inverse

In this paper, we investigate the fuzzy solutions of the complex fuzzy matrix equation (CFME) CZ˜=W˜, in which C is a complex crisp matrix, and W˜ is a complex fuzzy matrix. The purpose of this paper is three-fold. Firstly, the necessary and sufficient conditions for the existence of strong fuzzy solutions to the CFME are obtained using the MPWG inverse of the coefficient matrix. Secondly, we obtain a necessary and sufficient condition for the existence of S†,WG≥0 (S†,WG is called the Moore-Penrose weak group inverse of the coefficient matrix S) in order to obtain a strong fuzzy matrix solution of CFME. Moreover, general strong fuzzy solutions of the CFME are derived and an algorithm for obtaining general strong fuzzy solutions of CFME by the MPWG inverse is also established. Finally, some numerical examples are given to illustrate the main results.