Idempotent uninorms

Uninorms are an important generalization of t-norms and t-conorms, having a neutral element lying anywhere in the unit interval. Two broad classes of idempotent uninorms are fully characterized: the class of left-continuous ones and the class of right-continuous ones. In particular, the important subclasses of conjunctive left-continuous idempotent uninorms and of disjunctive right-continuous idempotent uninorms are characterized by means of super-involutive and sub-involutive decreasing unary operators. As a consequence, it is shown that any involutive negator gives rise to a conjunctive left-continuous idempotent uninorm and to a disjunctive right-continuous idempotent uninorm.