On the laws of contraposition for residual implications derived from overlap functions

Overlap functions are aggregation operators used in the overlap problem or when the associativity is not required. Residual implications derived from them (RO-implications) preserve the residuation property, and any overlap function O and the respective RO-implication form an adjoint pair, which is important in many applications. RO-implications are weaker than R-implications constructed from positive and continuous t-norms, since RO-implications do not necessarily satisfy certain properties, but only weaker versions of these properties. However, in general, such properties are not demanded for many applications. In this paper, we analyze the laws of contraposition for RO-implications with respect to a fuzzy negation.