FUZZY THRESHOLD FUNCTIONS AND APPLICATIONS

The set of fuzzy threshold functions is defined to be a fuzzy set over the set of functions. All threshold functions have full memberships i n this fuzzy set. Defines and investigates a distance measure between a non-linearly separable function and the set of all threshold functio ns. Defines an explicit expression for the membership function of a fu zzy threshold function through the use of this distance measure and fi nds three upper bounds for this measure. Presents a general method to compute the distance, an algorithm to generate the representation auto matically, and a procedure to determine the proper weights and thresho lds automatically. Presents the relationships among threshold gate net works, artificial neural networks and fuzzy neural networks. The resul ts may have useful applications in logic design, pattern recognition, fuzzy logic, multi-objective fuzzy optimization and related areas.