Cut sets of intuitionistic fuzzy sets

In this paper,firstly,it is stated that,an intuitionistic fuzzy sets is a L-fuzzy set,and a set of all intuitionistic fuzzy sets over X is a complete lattice.Secondly,the definitions of cut set on intuitionistic fuzzy sets and an intuitionistic nested set are given.Properties of cut sets,decomposition theorem,representation theorem of intuitionistic fuzzy sets are discussed.Finally,the relation between cut sets on intuitionistic fuzzy sets and an intuitionistic fuzzy subset of a group is discussed.It is proved that A is an intuitionistic fuzzy subset of a group G if and only if cut sets of A are subgroup of G.