Water-like anomalies in the core-softened systems: Dependence on the trajectory in density-temperature plane

► We analyze the anomalies in kinetic coefficients in the core-softened systems. ► We show that the anomalies depend on the trajectory in density-temperature plane. ► The applicability of the Rosenfeld entropy scaling to these systems is analyzed. ► The validity of the Rosenfeld scaling relation also depends on the trajectory.