Systematically investigates structures of fuzzy partitions. By means of the concept of cut sets of fuzzy sets a new expressibility theorem of fuzzy partition via classic partitions is proved. A method of inducing a fuzzy equivalence relation from a fuzzy partition is given. Based on the commonly used fuzzy partition in fuzzy control, the concepts of normal fuzzy partition and the corresponding characteristic function are defined, and the classical equivalence relation induced by normal fuzzy partition and an estimation of cardinality of equivalence classes are studied.

fuzzy partition; fuzzy equivalence relation; normal fuzzy partition