The associativity of n-dimensional copulas in the sense of Post is studied. These copulas are shown to be just n-ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.
S-measures are special fuzzy measures decomposable with respect to some fixed t-conorm S. We investigate the relationship of S-measures with some distinguished properties of fuzzy measures, such as subadditivity, submodularity, belief, etc. We show, for example, that each SP-measure is a plausibility measure, and that each S-measure is submodular whenever S is 1-Lipschitz.