Elsevier

Fuzzy Sets and Systems

Volume 160, Issue 6, 16 March 2009, Pages 726-732
Fuzzy Sets and Systems

On some construction methods for 1-Lipschitz aggregation functions

https://doi.org/10.1016/j.fss.2008.06.017Get rights and content

Abstract

Flipping method for constructing copulas from a given copula is extended to aggregation functions. Aggregation functions admitting flipping method are characterized and studied. Moreover, the algebraic structure of several kinds of dualities on aggregation functions, including the flipping method, the reverse method and the standard duality, is classified. Based on composition of construction methods, several new construction methods for 1-Lipschitz aggregation functions are introduced, and their algebraic relationships are studied.

References (8)

  • G. Beliakov, A. Pradera, T. Calvo, Aggregation functions: a guide for practitioners, Studies in Fuzziness and Soft...
  • T. Calvo et al.

    Aggregation functions: properties, classes and construction methods

  • E.P. Klement et al.

    Intervals of 1-Lipschitz aggregation functions, quasi-copulas and copulas with given affine section

    Monatsh. Math.

    (2007)
  • E.P. Klement et al.

    Invariant copulas

    Kybernetika

    (2002)
There are more references available in the full text version of this article.

Cited by (0)

View full text