The Law of Contraposition and the Law of Importation for Probabilistic S-Implications.

In 2011 Grzegorzewski introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic s-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this article we will focus on the law of contraposition and the law of importation for probabilistic s-implications.