Abstract:In this paper, on the basis of fuzzy quotient space theory, cluster analysis methods based on fuzzy similarity relations and normalized distance are proposed to solve data structure analysis of complex systems. Three conclusions are given: (1) the strictly clustering analysis theoretical description by introducing hierarchical structures of fuzzy similarity relation and normalized distance; (2) the effective and rapid clustering algorithms of their hierarchical structures; (3) a sufficient condition for isomorphic hierarchical structures. These conclusions are suitable to data structure analysis of all complex systems based on similarity relation.