Abstract
Copulas with given diagonals have been studied in [5, 11]. In [2, 6, 12] smallest and greatest (quasi-)copulas with given diagonals are constructed. Both (two-dimensional) copulas and quasi-copulas are special cases of binary 1-Lipschitz aggregation operators [3, 9]. We give constructions for smallest and greatest 1-Lipschitz aggregation operators with given diagonals, allowing us to obtain most results of [12] on (quasi-)copulas with given diagonals as special cases. In particular, the smallest (quasi-)copula with a given diagonal coincides with the smallest 1-Lipschitz aggregation operator with that diagonal.
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Klement, E.P., Kolesárová, A. (2004). 1-Lipschitz Aggregation Operators, Quasi-Copulas and Copulas with Given Diagonals. In: Soft Methodology and Random Information Systems. Advances in Soft Computing, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44465-7_24
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DOI: https://doi.org/10.1007/978-3-540-44465-7_24
Publisher Name: Springer, Berlin, Heidelberg
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