An implicit function theorem for regular fuzzy logic functions

摘要

Regular fuzzy logic functions are the functions f : |0, 1|~n→ |0, 1| that can be obtained by means of a finite number of compositions from a number of very simple starting functions, which are related to three-valued logic. In this work we prove that if a function/can be implicitly denned by a system of equations involving regular fuzzy logic functions, then fis itself a regular fuzzy logic function. The proof is based on results about regular Kleene algebras and Masao Mukaidono's characterization of regular logic functions.