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, u-surjective, nonincreasing set-valued function, which gives us a necessary condition for a uninorm to have continuous underlying functions. A sufficient condition for a uninorm to have continuous underlying operations is also given. Several examples are included.