Characterizations of Residual Implications Derived From Copulas

Residual implications derived from conjunctors are one of the most important fuzzy implications in fuzzy logic which possess interesting theoretical and practical properties. Copulas are a special kind of conjunctors that come from probability theory and statistics that have important applications in many fields. We mainly discuss residual implications derived from copulas in this article. We further specify the domain of variables in a characterization of residual implications derived from quasi-copulas. A characterization of residual implications derived from proper quasi-copulas is obtained, which provides a characterization of residual implications derived from copulas. Since that characterization is not intuitive enough, we give another characterization of residual implications derived from copulas by level sets, which provides a geometrical insight.

Automated summary

This article focuses on residual implications derived from copulas, which are a special type of conjunctors derived from probability theory and statistics. We provide a characterization of these residual implications by level sets, offering a geometrical insight into their properties and applications.