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Associative Copulas: A Survey

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Fuzzy Logic and Information Fusion

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 339))

Abstract

Copulas—functions that join multivariate distribution functions to their one-dimensional margins—are special cases of binary 1-Lipschitz aggregation functions, commonly used in aggregation processes. Here we consider a significant class of copulas: Associative copulas. We explore briefly the subclass of Archimedean copulas, and some of the properties and applications of associative copulas, such as the simultaneous associativity, the Kendall distribution functions, topological aspects, etc. Finally, some open problems are posed.

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Acknowledgments

The authors wish to thank two anonymous referees for helpful comments. The authors also acknowledge the support by the Ministerio de Economía y Competitividad (Spain) under research project MTM2014-60594-P.

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Authors and Affiliations

  1. Research Group of Mathematical Analysis, University of Almería, 04120, Almería, Spain

    Juan Fernández-Sánchez & Manuel Úbeda-Flores

  2. Department of Applied Mathematics, University of Granada, 18071, Granada, Spain

    José Juan Quesada-Molina

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  1. Juan Fernández-Sánchez
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  2. José Juan Quesada-Molina
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  3. Manuel Úbeda-Flores
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Correspondence to Manuel Úbeda-Flores .

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  1. University of Alcalá, Alcalá de Henares, Spain

    Tomasa Calvo Sánchez

  2. University of Balearic Islands, Palma, Spain

    Joan Torrens Sastre

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Fernández-Sánchez, J., Quesada-Molina, J.J., Úbeda-Flores, M. (2016). Associative Copulas: A Survey. In: Calvo Sánchez, T., Torrens Sastre, J. (eds) Fuzzy Logic and Information Fusion. Studies in Fuzziness and Soft Computing, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-319-30421-2_3

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