In this paper, the geometric meaning of the transitive closure of a fuzzy relation in corresponding fuzzy graph is first given. An optimal algorithm, which is based on the computation of graph connected components, for fuzzy classification problem is proposed. For any given n samples, the worst case time complexity T(n) of the algorithm satisfies that O(n)≤T(n)≤O(n²). Compared with the classic fuzzy classification algorithm, which is based on the computation of the transitive closure of a given relative matrix and of the O(n³log n) time, the new algorithm decreases O(nlog n) time factor at least. The theoretic analysis and computer performance show that the real computing time of the new algorithm is acceptable when it is used for fuzzy classification on large data.

国家863高科技发展计划资助项目(863-306-ZT06-01-4)；山东省自然科学基金资助项目(Z99G01)