Abstract
Copulas have been deeply investigated because of their applications in many fields. From the theoretical point of view, a key point in this research lies in the search of new construction methods of parametrized families of copulas. This paper presents some construction methods based on fuzzy implication functions by reversing the construction methods of fuzzy implication functions from copulas presented by P. Grzegorzewski in some recent papers. Specifically, the PSI and SSI-construction methods of copulas are proposed which provide copulas from a given fuzzy implication function. In addition, the analysis of these construction methods of copulas lead to the characterization of the intersection of the probabilistic S and survival S-implications with (S, N) and R-implications.
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This paper has been partially supported by the Spanish Grant TIN2013-42795-P.
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Massanet, S., Ruiz-Aguilera, D. & Torrens, J. On two construction methods of copulas from fuzzy implication functions. Prog Artif Intell 5, 1–14 (2016). https://doi.org/10.1007/s13748-015-0069-6
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DOI: https://doi.org/10.1007/s13748-015-0069-6