Fuzzy logic systems are equivalent to feedforward neural networks

Fuzzy logic systems and feedforward neural networks are equivalent in essence. First, interpolation representations of fuzzy logic systems are introduced and several important conclusions are given. Then three important kinds of neural networks are defined, i. e. linear neural networks, rectangle wave neural networks and nonlinear neural networks. Then it is proved that nonlinear neural networks can be represented by rectangle wave neural networks. Based on the results mentioned above, the equivalence between fuzzy logic systems and feedforward neural networks is proved, which will be very useful for theoretical research or applications on fuzzy logic systems or neural networks by means of combining fuzzy logic systems with neural networks.