On the Computational Power of Max-Min Propagation Neural Networks

We investigate the computational power of max-min propagation (MMP) neural networks, composed of neurons with maximum (Max) or minimum (Min) activation functions, applied over the weighted sums of inputs. The main results presented are that a single-layer MMP network can represent exactly any pseudo-Boolean function F:{0,1}n → [0,1], and that two-layer MMP neural networks are universal approximators. In addition, it is shown that several well-known fuzzy min-max (FMM) neural networks, such as Simpson's FMM, are representable by MMP neural networks.