On a class of transformations of copulas and quasi-copulas

Authors:
Elisabetta Alvoni;Pier Luigi Papini;Fabio Spizzichino
Affiliations:
Department of Mathematics for Economic and Social Sciences, University of Bologna, Viale Filopanti, 5, I 40126 Bologna, Italy;Department of Mathematics, University of Bologna, I 40126 Bologna, Italy;Department of Mathematics, University “La Sapienza”, I-00185 Rome, Italy
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 6
Cited 5

Two families of fuzzy integrals

Fuzzy Sets and Systems
A characterization of quasi-copulas

Journal of Multivariate Analysis
Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes

Journal of Multivariate Analysis
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)
A concept of duality for multivariate exchangeable survival models

Fuzzy Sets and Systems
Discrete Copulas

IEEE Transactions on Fuzzy Systems

A concept of duality for multivariate exchangeable survival models

Fuzzy Sets and Systems
Kendall distributions and level sets in bivariate exchangeable survival models

Information Sciences: an International Journal
Semi-copulas, capacities and families of level sets

Fuzzy Sets and Systems
On distance distribution functions-valued submeasures related to aggregation functions

Fuzzy Sets and Systems
Some results on a transformation of copulas and quasi-copulas

Information Sciences: an International Journal

Quantified Score

Hi-index	0.21

Visualization

Abstract

The theory of copulas is by now a very well established one. Recently, larger classes of functions C:[0,1]^n-[0,1], that are increasing in each variable and satisfy some conditions at the boundary (like quasi-copulas), have been the object of fruitful research. Several authors have considered the action of a class of transformations on some aggregation operators, as t-norms, copulas, quasi-copulas and so on. These simple transformations do not preserve in general all properties of copulas (or quasi-copulas): in particular, the fact that only some properties are preserved by these transformations, suggested the introduction of semi-copulas. The purpose of the present contribution is to give a fairly complete picture concerning such action on copulas and quasi-copulas; in particular, we prove results concerning inclusions and strict inclusions among these classes of operators, and those of their transforms.