Abstract
This paper presents a formalization of cluster extraction algorithms for an asymmetric fuzzy data, i.e. a fuzzy digraph. First, this paper classifies a fuzzy digraph into seven categories of fuzzy connectedness-1) strongly complete, 2) weakly complete, 3) bilaterally connected, 4) unilaterally connected, 5) strongly connected, 6) weakly connected, and 7) totally ordered digraphs. Second, extraction algorithms of subgraphs are presented according to respective 1)-6) connectivity categories. Then, it is shown that each cluster extraction algorithm operationally results in a clique extraction algorithm. Third, a minimum weakly complete digraph is defined and then an extraction algorithm based on totally ordered category is presented.
