关于Fuzzy群概念的一点注记

Fuzzy子广群和Fuzzy子群的概念是1971年由Rosenfeld1]给出的。本文用一个反例说明了匈牙利L·Filep在《Structureandconstructionoffuzzysubgroupsofagroup》一文2]中的命题“群G的Fuzzy子广群必是Fuzzy子群”是错误的。同时证明了当G为有限群时，G的Fuzzy子广群和Fuzzy子群的等价性。还指出文2]由上述错误命题推出的关于Fuzzy群的结构定理的证明是有问题的。事实上，它在有限群G条件下是成立的。此结果在1992年已经给出3]。

A Note of Concept of Fuzzy Group

The concept of Fuzzy groupid and Fuzzy subgroup is given by Rosenfeld in 1971/ Ac-cording to L. Filep the proposition, Fuzzy groupaid of group G implies be Fuzzy subgroup is proved to be wrong by a counter example employed in this these. The anthor also proves it inappropriate the proof of the structure of theorem of Infinite Fuzzy subgroup' which is inferred from the former in the paper (2). Under the condition of Finite Group, the author also obtained the structure of theorem in 1992.