Characterizations of Residual Implications Derived From Copulas
Characterizations of Residual Implications Derived From Copulas
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DOI：
10.1109/tfuzz.2022.3197902
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发表时间：
2023-04
影响因子：
11.9
通讯作者：
Wei Ji;Jiajia Xie
中科院分区：
文献类型：
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作者：
Wei Ji;Jiajia Xie
由合取子导出的剩余蕴涵是模糊逻辑中最重要的模糊蕴涵之一，具有有趣的理论和实用性质。Copula是概率论和统计学中的一种特殊的连接子，在许多领域有着重要的应用。本文主要讨论由Copula函数导出的剩余蕴涵。我们进一步指定域的变量在一个表征的残余影响来自准copula。给出了由真拟Copula导出的剩余蕴涵的一个刻画，从而给出了由拟Copula导出的剩余蕴涵的一个刻画。由于这种刻画不够直观，我们给出了水平集对Copula的剩余蕴涵的另一种刻画，这提供了一种几何上的见解。
Residual implications derived from conjunctors are one of the most important fuzzy implications in fuzzy logic which possess interesting theoretical and practical properties. Copulas are a special kind of conjunctors that come from probability theory and statistics that have important applications in many fields. We mainly discuss residual implications derived from copulas in this article. We further specify the domain of variables in a characterization of residual implications derived from quasi-copulas. A characterization of residual implications derived from proper quasi-copulas is obtained, which provides a characterization of residual implications derived from copulas. Since that characterization is not intuitive enough, we give another characterization of residual implications derived from copulas by level sets, which provides a geometrical insight.