Fuzzy threshold functions and applications

Abstract

The set of fuzzy threshold functions is defined to be a fuzzy set over the set of functions. All threshold functions have full memberships in this fuzzy set. Defines and investigates a distance measure between a non‐linearly separable function and the set of all threshold functions. Defines an explicit expression for the membership function of a fuzzy threshold function through the use of this distance measure and finds three upper bounds for this measure. Presents a general method to compute the distance, an algorithm to generate the representation automatically, and a procedure to determine the proper weights and thresholds automatically. Presents the relationships among threshold gate networks, artificial neural networks and fuzzy neural networks. The results may have useful applications in logic design, pattern recognition, fuzzy logic, multi‐objective fuzzy optimization and related areas.

Citation

Lee, E.T. and Chou, T. (1995), "Fuzzy threshold functions and applications", Kybernetes, Vol. 24 No. 7, pp. 99-122. https://doi.org/10.1108/03684929510095711