Title :
On the Number of Equivalent Classes of Fuzzy Subgroups of Finite Nilpotent Groups
Author :
Song, Mingjuan ; Feng, Yutie ; Zhao, Guoliang
Author_Institution :
Dept. of Math. & Mech., Heilongjiang Inst. of Sci. & Technol., Harbin
Abstract :
In this paper, we define an equivalent relation of fuzzy subgroups. That is, two F-subgroups are equivalent if they have the level sets with the same order.By means of studying synthesizseries and the chain of quotient group of a group as well as the chain of factors and the chain of quotient of a group´order, we obtain the formulas to find the number of equivalent classes of maximal fuzzy subgroups and fuzzy groups of a nilpotent group, at last we founded the relationships characterization of them.
Keywords :
fuzzy set theory; group theory; chain of factors; chain of quotient; chain of quotient group; equivalent classes; finite nilpotent groups; fuzzy groups; maximal fuzzy subgroups; Fuzzy control; Fuzzy sets; Level set; Mathematics;
Conference_Titel :
Innovative Computing Information and Control, 2008. ICICIC '08. 3rd International Conference on
Conference_Location :
Dalian, Liaoning
Print_ISBN :
978-0-7695-3161-8
Electronic_ISBN :
978-0-7695-3161-8
DOI :
10.1109/ICICIC.2008.400
