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
相关论文
共 50 条
  • [21] Compatibility of three bivariate quasi-copulas:: Applications to copulas
    Rodíguez-Lallena, JA
    Ubeda-Flores, M
    SOFT METHODOLOGY AND RANDOM INFORMATION SYSTEMS, 2004, : 173 - 180
  • [22] Freedom in constructing quasi-copulas vs. copulas
    Omladič, Matjaž
    Stopar, Nik
    Fuzzy Sets and Systems, 2025, 514
  • [23] ON THE CLASSES OF COPULAS AND QUASI-COPULAS WITH A GIVEN DIAGONAL SECTION
    Durante, Fabrizio
    Fernandez-Sanchez, Juan
    INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2011, 19 (01) : 1 - 10
  • [24] On the construction of copulas and quasi-copulas with given diagonal sections
    Nelsena, Roger B.
    Quesada-Molina, Jose Juan
    Rodriguez-Lallena, Jose Antonio
    Ubeda-Flores, Manuel
    INSURANCE MATHEMATICS & ECONOMICS, 2008, 42 (02): : 473 - 483
  • [25] DEFECTS AND TRANSFORMATIONS OF QUASI-COPULAS
    Dibala, Michal
    Saminger-Platz, Susanne
    Mesiar, Radko
    Klement, Erich Peter
    KYBERNETIKA, 2016, 52 (06) : 848 - 865
  • [26] On power stable quasi-copulas
    Kolesarova, Anna
    Mesiar, Radko
    PROCEEDINGS OF THE 8TH CONFERENCE OF THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY (EUSFLAT-13), 2013, 32 : 161 - 164
  • [27] Quasi-copulas and signed measures
    Nelsen, Roger B.
    Quesada-Molina, Jose Juan
    Rodriguez-Lallena, Jose Antonio
    Ubeda-Flores, Manuel
    FUZZY SETS AND SYSTEMS, 2010, 161 (17) : 2328 - 2336
  • [28] Quasi-copulas on discrete scales
    Mordelová, J
    COMPUTATIONAL INTELLIGENCE, THEORY AND APPLICATIONS, 2005, : 537 - 544
  • [29] Multivariate Archimedean quasi-copulas
    Nelsen, RB
    Quesada-Molina, JJ
    Rodríguez-Lallena, JA
    Ubeda-Flores, M
    DISTRIBUTIONS WITH GIVEN MARGINALS AND STATISTICAL MODELLING, 2002, : 179 - 185
  • [30] On the Structure of the Classes of Copulas and Quasi-Copulas with a Given Diagonal Section
    Fernandez-Sanchez, Juan
    Ubeda-Flores, Manuel
    INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 2020, 28 (03) : 513 - 524
12345