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有限Abel群的Fuzzy子群的等价分类及其类数 被引量:5

Equivalent Classes and Its Number of Fuzzy Subgroups of a Finite Abel Group
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摘要 定义Fuzzy子群的两种等价关系,给出了有限Abel群的Fuzzy子群在这两种等价关系下的等价类数的求解公式。 In this paper, two equivalence relationships on fuzzy subgroups of a group are defined, and the formulas to find the numbers of equivalent classes of fuzzy subgroups of a finite Abel group in two equivalence relationship are given.
机构地区 黑龙江科技学院
出处 《模糊系统与数学》 CSCD 北大核心 2005年第3期29-32,共4页 Fuzzy Systems and Mathematics
关键词 水平集的阶 合成群列 商群列 因数列 极大因数列 L等价 LO等价 The Order of a Level Set Composition Series of a Group Quotient Series of a Group Divisor Series of a Number Maximal Divisor Series of a Number L Equivalent Relationship~ LO Equivalent Relationship
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参考文献5

  • 1熊全淹.近世代数(第二版)[M].上海:上海科学出版社,1978..
  • 2宋明娟.有限循环群的Fuzzy子群的等价类数[J].模糊系统与数学,2003,17(3):77-79. 被引量:7
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二级参考文献8

  • 1lászló F.Structure and construction of fuzzy subgroups of a group[J].Fuzzy Sets and Systems,1992,51:105-109.
  • 2(美)赫尔.群论[M].北京:科学出版社,1982..
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  • 4Das P S.Fuzzy groups and level subgroups[J].J Math Anal Appl,1981,84:264-269.
  • 5lászlà F.Structure and construction of fuzzy subgroups of a group[J].Fuzzy Sets and Systems,1992,51:105~109.
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  • 7熊全淹.近世代数(第二版)[M].上海:上海科学出版社,1978..
  • 8(美)赫尔.群论[M].北京:科学出版社,1982..

共引文献7

同被引文献23

  • 1宋明娟.初等交换P-群的模糊子群的等价类数[J].黑龙江科技学院学报,2004,14(5):315-316. 被引量:2
  • 2陈彦恒,曹洪平.各阶非平凡子群的个数为p+1的p-群的完全分类[J].西南大学学报(自然科学版),2007,29(2):11-14. 被引量:10
  • 3Zadeh L A. Fuzzy set[J]. Inform. Control,1965,8:338-353.
  • 4Rosenfeld A. Fuzzy groups[J]. J. Math. Anal. Appl. , 1971,35 : 512-517.
  • 5Zhang Y J, Zhou K Q. A note on equivalence relation of fuzzy subgroups[J]. Fuzzy Sets and Systems, 1998,95:234 -247.
  • 6Laszlo F. Structure and construction of fuzzy subgroups of a group[J]. Fuzzy Sets and Systems, 1992,51:105-109.
  • 7Zadeh L A. Fuzzy set[J]. Inform. Control, 1965,8 : 338-353.
  • 8Rosenfeld A. Fuzzy groups[J]. J. Math. Anal. Appl, 1971,35 : 512-517.
  • 9Dixit V N, et al. Level subgroups and union of fuzzy subgroups[J]. Fuzzy Sets and Systems,1990,37:359-371.
  • 10Das P S. Fuzzy groups and level subgroups[J]. J. Math. Anal. Appl,1981,84:264-269.

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