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 workscomparing 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 aspecific family of fuzzy inference systems: Tagaki-Sugeno fuzzy inference systems (FIS)are nearly equivalent structure although FIS can be seen as slightly more generalincluding RBF as a result of some architectural options and simplifications. However thesmall differences which render FIS more general can lead to a different interpretation ofthe functioning of these methods. In order to resolve a problem more easily RBF projectsthe problem data into a new abstract space whereas FIS roughly try to decompose such aproblem and thus to allow for a lot of local operations, smoothly combined in someoverlapping regions. On the practical side, experimental comparisons will be presentedon Benchmark problems of classification and identification. Current results seem toindicate that while it is worth maintaining the more simple and less parametrized RBFfor problems of classification, the small structural additions leading to FIS can be ofinterest for function identification.