Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems

This short article shows that under some minor restrictions , the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on re presentational power, etc., can be applied to both models directly. It is of interest to observe that two models stemmi ng from different origins turn out to be functional equivale nt. This paper demonstrates the functional equivalence between radial basis function networks (RBFN’s) and a simplied class of fuzzy inference systems. Though these two models are motivated from different origins (RBFN’s from physiology and fuzzy inference systems from cognitive science), they share common characteristics not only in their operations on data, but also in their learning process to achieve desired mappings. We show that under some minor restrictions, they are functionally equivalent; the learning algorithms and the analysis on representational p ower for one model can be applied to the other, and vice versa.