Eurofuse 2011 pp 147-156 | Cite as

On a Generalization of the Notion of a Survival Copula

  • B. De Baets
  • H. De Meyer
  • R. Mesiar
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 107)

Abstract

We introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas, a well-studied class of binary aggregation functions with a profound probabilistic interpretation, to their associated survival copulas. The new transformation, called double flipping, is the composition of two elementary flipping transformations introduced earlier, each operating on one of the arguments of the aggregation function. We lay bare the relationships between these elementary flipping operations and double flipping. We characterize different subclasses of flippable aggregation functions, in particular aggregation functions that have an absorbing element or that have a neutral element. In this investigation, the key role played by quasi-copulas and their dual operations is highlighted. These findings support the introduction of the term survival aggregation function.

Keywords

Cumulative Distribution Function Representation Theorem Aggregation Function Neutral Element Dual Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • B. De Baets
    • 1
  • H. De Meyer
    • 2
  • R. Mesiar
    • 3
  1. 1.Dept of Applied Mathematics, Biometrics and Process ControlGhent UniversityGentBelgium
  2. 2.Dept of Applied Mathematics and Computer ScienceGhent UniversityGentBelgium
  3. 3.Dept of Mathematics and Descriptive GeometrySlovak University of TechnologyBratislavaSlovakia

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