Abstract
We discuss and stress the role of ultramodularity and Schur concavity in special types of constructions of copulas. After recalling some known ultamodularity-based results, we focus on the so-called D-product of a copula and its dual. We show that for each copula D which is ultramodular and Schur concave on the left upper triangle of the unit square, this D-product of an arbitrary copula and its dual is again a copula. Several examples and counterexamples are given. Finally, some of our results are generalized to the case of semicopulas and quasi-copulas.
| Original language | English |
|---|---|
| Pages (from-to) | 361-381 |
| Number of pages | 21 |
| Journal | Journal of Mathematical Inequalities |
| Volume | 11 |
| DOIs | |
| Publication status | Published - 2017 |
Fields of science
- 101 Mathematics
- 101013 Mathematical logic
- 101024 Probability theory
- 102001 Artificial intelligence
- 102003 Image processing
- 102019 Machine learning
- 603109 Logic
- 202027 Mechatronics
JKU Focus areas
- Computation in Informatics and Mathematics
- Mechatronics and Information Processing
- Nano-, Bio- and Polymer-Systems: From Structure to Function