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
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