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Abstract

Intuitutionistic fuzzy ( Open image in new window F ) set is a generalization of the concept fuzzy set. Intuitutionistic fuzzy group is Open image in new window F set with a kind of operation. However, few of structure of Intuitutionistic fuzzy groups ( Open image in new window FGs) are known. Aimed at this, this paper gives and proves four theorems about some structures as follows: 1.Caushy theorem of Open image in new window F groups. 2. The sufficient and necessary condition of an Open image in new window F p-group is that the order of Open image in new window F group is a power of p. 3.The number of elements of conjugate class in Open image in new window FG group equals the number of cosets in Open image in new window F quotient group. And 4.The condition that there exist fixed element in conjugate class in Open image in new window FG group and the number of fixed elements. Compared with relative works, The sets and operations of classical groups are classical. In this paper, the sets are Open image in new window FSs and the operations are based on Open image in new window F relation. The similar works in this paper have not be seen in available Open image in new window F groups.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Chuanyu Xu
    • 1
  1. 1.Department of MathZhejiang Gongshang UniversityHangzhouChina

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