The Best Interval Representation of Fuzzy S-Implications and Automorphisms

Abstract

The aim of this work is to analyze interval fuzzy S-implications and interval automorphisms. Starting from any fuzzy S-implication, it is shown how to obtain an interval fuzzy S-implication canonically. We proved that such interval fuzzy S-implications meet the optimality property and preserve the same properties satisfied by fuzzy S-implications. In addition, commutative diagrams are used in order to relate fuzzy S-implications to interval fuzzy S-implications, and to understand how interval automorphisms act on interval S-implications, generating other interval fuzzy S-implications.