Characterization of n-uninorms with continuous underlying functions via z-ordinal sum construction

Abstract

The n-uninorms with continuous underlying t-norms and t-conorms are characterized via the z-ordinal sum construction. We show that each n-uninorm with continuous underlying t-norms and t-conorms can be expressed as a z-ordinal sum of a countable number of Archimedean and idempotent semigroups with respect to the branching set A∼{z1,…,zn−1}, where the corresponding partial order has a tree structure.