Abstract
On a continuous logic system whcih uses AND, OR, NOT and arithmetic operations, one type of infinitelly-valued functions : infinitelly-valued threshold functions were defined in previous papers. It has been shown that the infinitelly-valued functions may be applied to approximate reasoning involving ambiguity, and to process control with high speed, while there remains a fundamental problem of devising and effective scheme to express non-liear approximate reasoning rules by teh infinitelly-valued threshold functions.This paper firstly discusses mathematical aspects of a group of the infinitelly-valued threshold functions, which have range of the interval [0,1] as I/O domain and are denominated the fuzzy threshold functions. Secondly, particular fuzzy threshold functions, which behave as discrete threshold functions when discrete inputs are given, are discussed, Necessary and sufficient conditions are presented. Thirdly, multistage synthesis of the infinitelly-valued threshold functions are discussed showing what type of functions may be generated. Based on these considerations, this section clarifies the applicability of the infinitelly-valued threshold functions to express non-linear approximate reasoning rules. Lastly, a synthesis method of an analogue full-adder is proposed as an application of these considerations.
