Isaac Rudnick, California Polytechnic State University, USA

By Zadehs original formulation, likelihood distributions can be seen as a unique kind of fuzzy set whose logical operations have meaningful probabilistic interpretations. In this work, we develop a variant of this fuzzy set in which an arbitrary number of fuzzy logic operations may be applied without increasing the space and time required for membership evaluation. By using a band-limited Fourier series approximation for a truncated Gaussian kernel, we also demonstrate a significant reduction in time and space requirements for mixture model evaluation. Probabilistic and fuzzy set interpretations, as well as benchmarks against Standard Additive Models (SAMs) are provided along with an analysis of complexity and scaling properties.

fuzzy sets, fuzzy logic, standard additive models, gaussian mixture models, fourier series, fourier basis density models