Comparing RBF and Fuzzy Inference Systems on theoretical and practical basis

This paper aims at helping to clarify the current confusion raised by a lot of works comparing or merging neural net with fuzzy inference systems. On the theoretical side, we first show that a specific family of neural nets: Radial-Basis Functions (RBF) and a specific family of fuzzy inference systems: Tagaki-Sugeno fuzzy inference systems (FIS) are nearly equivalent structure although FIS can be seen as slightly more general including RBF as a result of some architectural options and simplifications. However the small differences which render FIS more general can lead to a different interpretation of the functioning of these methods. In order to resolve a problem more easily RBF projects the problem data into a new abstract space whereas FIS roughly try to decompose such a problem and thus to allow for a lot of local operations, smoothly combined in some overlapping regions. On the practical side, experimental comparisons will be presented on Benchmark problems of classification and identification. Current results seem to indicate that while it is worth maintaining the more simple and less parametrized RBF for problems of classification, the small structural additions leading to FIS can be of interest for function identification.