A correlation between fuzzy logic systems (FLS) and zeroing neural networks (ZNN) design is investigated. It is shown that the gain parameter included in ZNN design can be dynamically adjusted over time by means of an appropriate value derived as the output of a properly defined FLS which includes appropriately defined membership functions and fuzzy logic rules. Dynamical systems which are applicable to time-varying rank-deficient matrices are proposed. Convergence properties are investigated and illustrative simulation experiments are performed. Presented simulation experiments confirm the superiority of the FLS proposed in the paper with respect to previously proposed FLS for dynamic adjustment of gain parameters. Furthermore, the superiority of the FLS-based ZNN model over the corresponding ZNN models based on the classical approach in defining the varying-gain parameter is demonstrated.