Ordinal sum constructions for aggregation functions on the real unit interval
Publish place: Iranian Journal of Fuzzy Systems، Vol: 19، Issue: 1
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-19-1_008
تاریخ نمایه سازی: 28 آذر 1400
Abstract:
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.
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Authors
A. Mesiarova-Zemankova
Mathematical Institute, Slovak Academy of Sciences, ۸۱۴ ۷۳ Bratislava, Slovakia
R. Mesiar
Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology, ۸۱۳۶۸ Bratislava, Slovakia
Y. Su
School of Mathematics Sciences, Suzhou University of Science and Technology, Suzhou ۲۱۵۰۰۹, China