On additive generators of overlap functions

In this paper we introduce the notion of additive generator pair for overlap functions. We also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair. In particular, given a continuous and positive t-norm T, we analyze the overlap functions which are obtained by the distortion of T by a pseudo-automorphism, showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo-automorphism and the additive generator of T. Finally, we also consider the influence of the migrativity, homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs.