Quasi-Copulas, Copulas and Fuzzy Implicators

被引：2
|
作者：
Mesiar, Radko [1 ,2 ]
Kolesarova, Anna [3 ]
机构：
[1] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, Fac Civil Engn, Radlinskeho 11, Bratislava 81005, Slovakia
[2] Univ Ostrava, Inst Res & Applicat Fuzzy Modelling, 30 Dubna 22, Ostrava 70103, Czech Republic
[3] Slovak Univ Technol Bratislava, Fac Chem & Food Technol, Inst Informat Engn Automat & Math, Radlinskeho 9, Bratislava 81237, Slovakia
来源：
INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS | 2020年 / 13卷 / 01期
关键词：
Copula; Fuzzy conjunctor; Fuzzy implicator; Quasi-copula; Semicopula; CONSTRUCTION;
D O I：
10.2991/ijcis.d.200527.004
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy implicators. A similar relation holds for copulas and 2-increasing 1-Lipschitz fuzzy implicators. Based on these relations, we introduce, discuss and exemplify several new construction methods for fuzzy implicators, and also discuss several dualities on the class of all 1-Lipschitz fuzzy implicators. In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some of its special cases. (C) 2020 The Authors. Published by Atlantis Press SARL.
引用
收藏
页码：681 / 689
页数：9
相关论文
共 50 条
  • [1] Quasi-Copulas, Copulas and Fuzzy Implicators
    Radko Mesiar
    Anna Kolesárová
    International Journal of Computational Intelligence Systems, 2020, 13 : 681 - 689
  • [2] Compositions of copulas and quasi-copulas
    Durante, F
    Sempi, C
    SOFT METHODOLOGY AND RANDOM INFORMATION SYSTEMS, 2004, : 189 - 196
  • [3] Transformations of copulas and quasi-copulas
    Klement, EP
    Mesiar, R
    Pap, E
    SOFT METHODOLOGY AND RANDOM INFORMATION SYSTEMS, 2004, : 181 - 188
  • [4] Fuzzy implicators related to (quasi-)copulas
    Kolesarova, Anna
    Mesiar, Radko
    PROCEEDINGS OF THE 11TH CONFERENCE OF THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY (EUSFLAT 2019), 2019, 1 : 235 - 240
  • [5] Multivariate copulas, quasi-copulas and lattices
    Fernandez-Sanchez, Juan
    Nelsen, Roger B.
    Ubeda-Flores, Manuel
    STATISTICS & PROBABILITY LETTERS, 2011, 81 (09) : 1365 - 1369
  • [6] Quasi-copulas and copulas on a discrete scale
    Kolesárová, A
    Mordelová, J
    SOFT COMPUTING, 2006, 10 (06) : 495 - 501
  • [7] Quasi-copulas as linear combinations of copulas
    Dolinar, Gregor
    Kuzma, Bojan
    Stopar, Nik
    FUZZY SETS AND SYSTEMS, 2024, 477
  • [8] On the α-migrativity of semicopulas, quasi-copulas, and copulas
    Mesiar, R.
    Bustince, H.
    Fernandez, J.
    INFORMATION SCIENCES, 2010, 180 (10) : 1967 - 1976
  • [9] Quasi-copulas and copulas on a discrete scale
    A. Kolesárová
    J. Mordelová
    Soft Computing, 2006, 10 : 495 - 501
  • [10] On a class of transformations of copulas and quasi-copulas
    Alvoni, Elisabetta
    Papini, Pier Luigi
    Spizzichino, Fabio
    FUZZY SETS AND SYSTEMS, 2009, 160 (03) : 334 - 343
12345