Quasi-Copulas, Copulas and Fuzzy Implicators
Radko Mesiar, Anna Kolesárová
International Journal of Computational Intelligence Systems · 2020
doi:10.2991/ijcis.d.200527.004 (opens in a new tab)
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Abstract
In this paper, we study relations between fuzzy implicators and some kinds of fuzzy conjunctors, in particular, quasi-copulas and copulas. We show that there is a one-to-one correspondence between the classes of all quasi-copulas and 1-Lipschitz fuzzy implicators. A similar relation holds for copulas and 2-increasing 1-Lipschitz fuzzy implicators. Based on these relations, we introduce, discuss and exemplify several new construction methods for fuzzy implicators, and also discuss several dualities on the class of all 1-Lipschitz fuzzy implicators. In addition, we introduce a construction method for fuzzy implicators based on any two copulas and a Lebesgue integrable fuzzy implicator, and discuss some of its special cases.
Abstract licence: CC BY-NC-ND
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