  Overlap functions were introduced as class of bivariate aggregation functions
on [0, 1] to be applied in image processing. This paper has as main objective
to present appropriates definitions of overlap functions considering the scope
of lattices and introduced a more general definition, called of quasi-overlaps,
which arise of abolishes the continuity condition. In addition, are
investigated the main properties of (quasi-)overlaps on bounded lattices,
namely, convex sum, migrativity, homogeneity, idempotency and cancellation law.
Moreover, we make a characterization of Archimedian overlaps.
