Title :
Functional equivalence between neural networks and fuzzy systems with sinusoidal membership functions
Author :
Jin, Liang ; Gupta, Madan M.
Author_Institution :
Intelligent Syst. Res. Lab., Saskatchewan Univ., Saskatoon, Sask., Canada
Abstract :
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
Keywords :
feedforward neural nets; fuzzy neural nets; fuzzy systems; multilayer perceptrons; centroid defuzzifier; functional equivalence; fuzzy basis function networks; graded value; input-output equations; multi-input single-output fuzzy systems; multilayered neural networks; normalized structure; product inference; singleton fuzzifier; sinusoidal membership function; universal approximation capability; Artificial neural networks; Educational institutions; Equations; Fuzzy systems; Intelligent networks; Intelligent systems; Laboratories; Multi-layer neural network; Neural networks; Neurons;
Conference_Titel :
Uncertainty Modeling and Analysis, 1995, and Annual Conference of the North American Fuzzy Information Processing Society. Proceedings of ISUMA - NAFIPS '95., Third International Symposium on
Conference_Location :
College Park, MD
Print_ISBN :
0-8186-7126-2
DOI :
10.1109/ISUMA.1995.527712
