Several Findings About the Weak Dominance Between <i>t</i> -Norms and Semi- <i>t</i> -Operators

Weak domination (WD, for short) is a specific relationship between binary operations that is intimately associated with domination relation. In this article, we investigate the WD between t-norms and semi-t-operators. Initially, our result reveals that no t-norm exists to weakly dominate a semi-t-operator. Next, we present the fundamental conditions under which semi-t-operators weakly dominate minimum t-norm [Formula: see text]. Lastly, we determine the necessary and sufficient conditions that enable semi-t-operators with the underlying continuous Archimedean operators to weakly dominate continuous Archimedean t-norms.