Concept Extensions and Weak Clusters Associated with Multiway Dissimilarity Measures

摘要

We consider contexts with a finite set of entities described in a poset. When entity descriptions belong to a meet-semilattice, we show that nonempty extensions of concepts assigned to such a context coincide with weak clusters associated with pairwise or multiway dissimilarity measures satisfying some compatibility condition. Moreover, by duality principle, when entity descriptions belong to a join-semilattice, a similar result holds for so-called dual concepts of the given context.