Characterization of idempotent n-uninorms

Abstract

The structure of idempotent n-uninorms is studied. We show that each idempotent 2-uninorm can be expressed as an ordinal sum of an idempotent uninorm (possibly also of a countable number of idempotent semigroups with operations min and max) and a 2-uninorm from Class 1 (possibly restricted to open or half-open unit square). Similar results are shown also for idempotent n-uninorms. Further, it is shown that idempotent n-uninorms are in one-to-one correspondence with special lower semi-lattices defined on the unit interval. The z-ordinal sum construction for partially ordered semigroups is also defined.