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The Preisach model, which is formulated as a weighted superposition of hysteresis kernels, has been widely used for hysteresis modeling, especially in smart-material-based actuators. However, in the classical Preisach model, a trade-off is always required between the model accuracy and the number of the hysteresis kernels. To deal with this problem, a model order reduction technique based on the discrete empirical interpolation method (DEIM) has recently been proposed. The method can largely reduce the number of the hysteresis kernels while barely losing the model accuracy. It is noted that the kernel weight in the reduced DEIM-based model can be both positive and negative, which means that the monotonicity of the Preisach model could be lost. The monotonicity is a very important property especially when constructing the inverse Preisach model. Furthermore, the loss of the monotonicity can also deteriorate the model predictability. In the current paper, a modification strategy is proposed. In the modified reduced Preisach model, the DEIM is only employed to select the dominant hysteresis kernels while the corresponding weights of the selected hysteresis kernels are re-identified by solving a constraint optimization problem. Systematic simulation studies and experimental validation are carried out to demonstrate the effectiveness of the proposed strategy.