On the lattice structure of the set of supermodular quasi-copulas

Abstract We study the relationship between the poset of supermodular n-quasi-copulas and the posets of n-quasi-copulas and n-copulas. It is known that, for n ⩾ 3 , the poset of n-quasi-copulas is not order-isomorphic to the Dedekind–MacNeille completion of the poset of n-copulas. We complement the latter result by showing that, for n ⩾ 3 , the structure of the poset of n-quasi-copulas is more closely related to that of the poset of supermodular n-quasi-copulas than that of the poset of n-copulas.

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