The equivalence between fuzzy logic systems and feedforward neural networks

Abstract

This paper demonstrates that fuzzy logic systems and feedforward neural networks are equivalent in essence. First, we introduce the concept of interpolation representations of fuzzy logic systems and several important conclusions. We then define mathematical model for rectangular wave neural networks and nonlinear neural networks. With this definition, we prove that nonlinear neural networks can be represented by rectangular wave neural networks. Based on this result, we prove the equivalence between fuzzy logic systems and feedforward neural networks. This result provides us a very useful guideline when we perform theoretical research and applications on fuzzy logic systems, neural networks, or neuro-fuzzy systems.