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Associative \(n\)-dimensional copulas. (English) Zbl 1225.03071
Associativity of \(n\)-ary functions \(F\) (in the sense of Post) possessing a neutral element \(e\) is shown to be equivalent to the classical associativity of related binary functions \(f\), so that the \(F\)s are the genuine \(n\)-ary extensions of \(f\)s. Based on this result, an open problem of the characterization of associative \(n\)-dimensional copulas is completely solved.

MSC:
03E72 Theory of fuzzy sets, etc.
26B35 Special properties of functions of several variables, Hölder conditions, etc.
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