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

被引：15

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

页码：89 / 99

页数：11

共 41 条

[1] ON THE CHARACTERIZATION OF A CLASS OF BINARY OPERATIONS ON DISTRIBUTION-FUNCTIONS [J].