Can Neural Networks Trained with 2-valued Logical Operations Simulate Fuzzy Logical Operations? (No.3)

Abstract

A human’s logical information processing seems simulated on the neural network in the brain. We trained 2-valued logical operations "and," "or" and "exclusive or" with a standard multi-layered neural network with the sigmoid function as activate function. We had similar results to those of fuzzy logical operations. In this paper we learn the "not" operation and show its results. The results of leaning depend on the activate functions. We propose a new activate function based on the S-function for defining fuzzy sets and show the results.