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

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 similar to{z(1), ..., z(n-1)}, where the corresponding partial order has a tree structure. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The n-uninorms with continuous underlying t-norms and t-conorms are characterized using the z-ordinal sum construction. It is shown that each of these uninorms can be expressed as a z-ordinal sum of a countable number of Archimedean and idempotent semigroups with respect to a branching set A, similar to {z(1), ..., z(n-1)}, where the corresponding partial order has a tree structure.