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Hierarchical clustering using transitive closure and semi-supervised classification based on fuzzy rough approximation

This paper studies a hierarchical rough classification alias fuzzy rough classification as a family of upper approximations. A hierarchical rough classification is related to the single linkage clustering by using the max-min transitive closure of a symmetric relation. Moreover, the approximations naturally are related to semi-supervised classifications. As an extension, a hierarchical rough classification that is symmetric and transitive, but not necessarily reflexive is considered, which is related to another method of clustering. Although this paper is theoretical, an illustrative example is given to observe a relation between hierarchical classification and semi-supervised clustering.