The unwalked path between quasi-copulas and copulas: Stepping stones in higher dimensions

被引：13
|
作者：
Arias-Garcia, J. J. [1 ]
Mesiar, R. [2 ,3 ]
De Baets, B. [1 ]
机构：
[1] Univ Ghent, KERMIT, Dept Math Modelling Stat & Bioinformat, Coupure Links 653, B-9000 Ghent, Belgium
[2] Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math & Descript Geometry, Radlinskeho 11, Bratislava 81005, Slovakia
[3] Palacky Univ, Fac Sci, Dept Algebra & Geometry, 17 Listopadu 12, Olomouc 77146, Czech Republic
来源：
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2017年 / 80卷
关键词：
n-quasi-copula; n-copula; Aggregation function; Lipschitz continuity; Supermodularity; n-increasingness; BOUNDS; INEQUALITIES; TRANSITIVITY; SETS;
D O I：
10.1016/j.ijar.2016.08.009
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We show that as the dimensionality increases, more and more interesting classes of operations can be identified between the class of n-quasi-copulas and the class of n-copulas. One such class is the class of supermodular n-quasi-copulas. We observe that some properties of 2-copulas that cannot be generalized to higher-dimensional copulas, hold true for supermodular n-quasi-copulas. Additionally, we show that trying to generalize a volume-based characterization of bivariate copulas to higher dimensions, results in a restrictive class of n-quasi-copulas. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：89 / 99
页数：11
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