Ordinal sum constructions for aggregation functions on the real unit interval

Document Type : Research Paper


1 Mathematical Institute, Slovak Academy of Sciences, 814 73 Bratislava, Slovakia

2 Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology, 81368 Bratislava, Slovakia

3 School of Mathematics Sciences, Suzhou University of Science and Technology, Suzhou 215009, China


We discuss ordinal sums as one of powerful tools in the aggregation theory serving, depending on the context, both as a construction method and as a representation, respectively. Up to recalling of several classical results dealing with ordinal sums, in particular dealing, e.g.,  with continuous t-norms, copulas, or recent results, e.g., concerning uninorms with continuous underlying functions, we present also several new results, such as the uniqueness of the link between t-norms or t-conorms, and related Archimedean components, problems dealing with the cardinality of the considered index sets in ordinal sums, or infinite ordinal sums of aggregation functions covering by one type of ordinal sums both t-norms and t-conorms ordinal sums.