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. © 2008 Elsevier B.V. All rights reserved.

On a class of transformations of copulas and quasi-copulas / Elisabetta, Alvoni; Pier Luigi, Papini; Spizzichino, Fabio. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 160:3(2009), pp. 334-343. [10.1016/j.fss.2008.03.025]

On a class of transformations of copulas and quasi-copulas

SPIZZICHINO, Fabio
2009

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. © 2008 Elsevier B.V. All rights reserved.
2009
construction of semi-copulas; distorsions; level curves of survival functions; semi-copulas; semi-copulas.; t-norms; transformations of copulas and quasi-copulas
01 Pubblicazione su rivista::01a Articolo in rivista
On a class of transformations of copulas and quasi-copulas / Elisabetta, Alvoni; Pier Luigi, Papini; Spizzichino, Fabio. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - STAMPA. - 160:3(2009), pp. 334-343. [10.1016/j.fss.2008.03.025]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/40917
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