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Extremal Lipschitz continuous aggregation functions with a given diagonal section
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DOI：10.1016/j.fss.2017.12.014.png)
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Abstract
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In this paper we study the smallest and the greatest M-Lipschitz continuous n-ary aggregation functions with a given diagonal section. We show that several properties that were studied for the smallest and the greatest 1-Lipschitz continuous binary aggregation functions with a given diagonal section extend naturally to higher dimensions while considering different Lipschitz constants. Just as in the binary case, we show that the smallest n-quasi-copula with a given diagonal section coincides with the smallest 1-Lipschitz n-ary aggregation function with that diagonal section. Additionally, we show that the smallest n-quasi-copula with a given diagonal section, called the Bertino n-quasi-copula, is supermodular for any n >= 2. (C) 2018 Elsevier B.V. All rights reserved.
Keywords:
n-Quasi-copula
n-Copula
Aggregation function
Lipschitz continuity
Supermodularity
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