Functional equivalence between neural networks and fuzzy systems with sinusoidal membership functions
Liang Jin, Μ.Μ. Gupta · 2002
The functional equivalence between multilayered neural networks (MNNs) and fuzzy systems with a singleton fuzzifier, a product inference, a centroid defuzzifier and a sinusoidal membership function is discussed in this paper. First, a normalized structure of MNNs is given in terms of input-output equations of MNNs. Fuzzy basis function network (FBFN) expansions of multi-input single-output (MISO) fuzzy systems are then given in order to describe the input-output relationships of fuzzy systems. Sinusoidal membership functions are introduced for fuzzy systems with a graded value over [0,1]. Functional equivalence between the two systems is analytically shown. Finally, the universal approximation capability of FBFNs is briefly discussed.