The weak dominance between t-norms and t-conorms revisited

The weak dominance relation between two binary operations was introduced as an extension of the dominance relation and the modularity equation. This paper continues the study of the weak dominance between t-norms and t-conorms. First, we present the characterization of the weak dominance of a nilpotent t-norm over a continuous Archimedean t-norm. Second, we establish the generalized sufficient and necessary conditions for the weak dominance of continuous t-norms over continuous t-norms. Finally, we obtain a generalized characterization of a continuous t-conorm weakly dominating a continuous t-norm by showing that $S_M$ weakly dominates any t-norm.