%0 Journal Article
%T Ordinal sum constructions for aggregation functions on the real unit interval
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Mesiarova-Zemankova, A.
%A Mesiar, R.
%A Su, Y.
%D 2022
%\ 02/01/2022
%V 19
%N 1
%P 83-96
%! Ordinal sum constructions for aggregation functions on the real unit interval
%K Ordinal sum
%K t-norm
%K t-conorm
%K uninorm
%R 10.22111/ijfs.2022.6553
%X 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.
%U https://ijfs.usb.ac.ir/article_6553_6beeac25621da8d6e197c370d729fd2c.pdf