A class of copulas with piecewise linear horizontal sections

We introduce the class of bivariate copulas with piecewise linear horizontal sections whose graph is composed, at most, of two segments. It is a wide class of copulas which contains some known copulas. We study several properties of the copulas in the new class concerning absolute continuity, singular components, measures of association, concordance ordering, dependence concepts and symmetry. Finally, we provide several examples.