N-contrapositivisation of fuzzy implication functions

Abstract

The law of contraposition with respect to a negation (usually strong) is one of the most studied properties in the theory of fuzzy implication functions. We already know some methods for modifying an implication with the aim that the new implication satisfies this property, these methods are called contrapositivisation. In this paper we present two new methods of contrapositivisation with respect to any strong negation and we study their properties. Along this study we will see that these new methods not only preserve the usual properties preserved by the already known methods, but they also have some additional property.