Les t-normes en logique multivalente : un théorème de représentation de l’ABOP


This paper considers the framework of a many-valued logic using a finite and totally ordered set of truth degrees, denoted LM. It proposes a study of a configurable aggregation operator, called ABOP, 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 t-norm in LM, showing ABOP is a generalisation of tnorm operators. Furthermore, it specifies the corresponding parameter values, defined by the residuated implication associated in LM to the considered t-norm. The paper then considers examples of classical fuzzy logic tnorms, adapted to LM, and examines the corresponding parameters, as instantiations of the general representation theorem.