Characterization of uninorms with continuous underlying t-norm and t-conorm by their set of discontinuity points

Uninorms with continuous underlying t-norm and t-conorm are discussed and properties of the set of discontinuity points of such a uninorm are shown. This set is proved to be a subset of the graph of a special symmetric, surjective, non-increasing multi-function. A sufficient condition for a uninorm to have continuous underlying operations is also given. Several examples are included.