An implicit function theorem for regular fuzzy logic functions

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 f can be implicitly defined by a system of equations involving regular fuzzy logic functions, then f is 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.