An Implicit Fuction Theorem for Regular Fuzzy Logic Functions

CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO

FUZZY SETS AND SYSTEMS

Año: 2007

0165-0114

Regular fuzzy logic functions are the functions f : [0,1]^n -> [0,1] that can be obtained by means of a .nite 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 ofregular logic funtions.