Abstract
Intuitutionistic fuzzy sets (simply, ϑ°FS) are a generalization of Fuzzy sets. Defining operations of sets by ϑ°FS, a new type of intuitutionistic fuzzy groups (ϑ°FS) is obtained. However, a few of properties of structure of ϑ°FS are known. Aimed at this, this paper forwards four theorems about ϑ°FS:1. the condition of subset is subgroup in ϑ°FS:2. ϑ°FS homomorphic image of ϑ°FS subgroup is ϑ°FS subgroup; 3.a kernel of homomorphism is normal subgroup; 4. the ϑ°FS homomorphic theorem. The work by this paper is different from the classical groups. In the former, the operations are ϑ°FS operations. In the latter, the operations are classical. This paper enriches the structural properties of ϑ°FS.
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