The discrete Preisach model is popular to describe the hysteresis of smart materials, such as the piezoelectric and ferroelectric material. Re-explaining the discrete Preisach model of antiferroelectric materials after introducing an extended Preisach function, the special multilayer perceptrons with only two input nodes was designed intrinsically to satisfy the anticommutative property of hysteresis without superfluous hidden nodes (called aMLP), where its output equals to the difference between two predictive results that two signals in the normal and reverse sequence are imported to the aMLP model. Several training algorithms, including the normal/hybrid generic algorithm (GA) and the normal/hybrid particle swarm optimization (PSO), were used to adjust the parameters of the aMLP model, respectively. The comparing results indicate that the aMLP models designed with the winner operation function pair of [tanh, ReLU] and trained by both normal and hybrid PSO algorithms suggest the better performance when applying the working voltages more than 50 V according to the experimental data. It provides another accurate way for an aMLP model to estimate the anticommutative property of hysteresis of smart materials.