T-norms in Many-Valued Logics: a Representation Theorem in the ABOP Framework

Marie-Jeanne Lesot, Adrien Revault d'Allonnes

Abstract: This paper proposes a study of a configurable aggregation operator in many-valued logic (MVL), called ABOP, standing for ABating OPerator. It focuses on its capacity of implementing any t-norm: the paper’s main theorem offers a constructive proof of the existence of a configuration for any given MVL t-norm, showing it is a generalisation of t-norm operators. Furthermore, it specifies the corresponding parameter values. The paper then considers several examples of classical fuzzy logic t-norms adapted to MVL, and examines the corresponding parameters, as instantiation of the general representation theorem.