Characterizations of idempotent n-ary uninorms

peer reviewedIn this paper we provide a characterization of the class of idempotent n-ary uninorms on a given chain. When the chain is finite, we also provide anaxiomatic characterization of the latter class by means of four conditions only: associativity, quasitriviality, symmetry, and nondecreasing monotonicity. In particular, we show that associativity can be replaced with bisymmetry in this axiomatization