The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-229

“Fuzzy Basis Functions: Comparisons with Other Basis Functions”

by Hyun M. Kim and Jerry M. Mendel

January 1993

Fuzzy basis functions (FBF's) which have the capability of combining both numerical data and linguistic information, are compared with other basis functions. Because a FBF network is different from other networks in that it is the only one that can combine numerical and linguistic information, comparisons are made when only numerical data is available. In particular, a FBF network is compared with a radial basis function (RBF) network from the viewpoint of function approximation. Their architectural interrelationships are discussed. Additionally, a RBF network, which is implemented using a regularization technique, is compared with a FBF network from the viewpoint of overcoming ill-posed problems. A FBF network is also compared with Specht's Probabilistic Neural Network and his General Regression Neural Network (GRNN) from an architectural point of view. This is motivated by the similarities of the FBF and GRNN formulas. Then, a FBF network is compared with a Gaussian sum approximation in which Gaussian functions play a central role. Finally, we summarize the architectural relationships between all the networks discussed in this paper, and compare the different approximations from the point of view of the assumptions made about the available data.

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