Some results on the weak dominance between t-norms and t-conorms

Abstract

In this study, we discuss the weak dominance relation between two binary operations which is closely related with the dominance relation. First, we present some basic properties of the weak dominance and prove that there exists no t-norm weakly dominating a t-conorm. Then we provide the necessary and sufficient conditions of a t-conorm weakly dominating a t-norm for different cases: both are Archimedean or ordinal sums. Lastly, the weak dominance between t-norms is discussed.