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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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##### References:
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