An implicit function theorem for regular fuzzy logic functions

Authors:
Miguel Campercholi;Diego Vaggione
Affiliations:
Fa.M.A.F., Universidad Nacional de Córdoba, Córdoba, Argentina;Fa.M.A.F., Universidad Nacional de Córdoba, Córdoba, Argentina
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

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.