IDEMPOTENT UNINORMS ON FINITE ORDINAL SCALES
Bernard De Baets, Janos C. Fodor, Daniel Ruiz-Aguilera, Joan David Janer Torrens · International Journal of Uncertainty Fuzziness and Knowledge-Based Systems · 2009
In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.