IJPAM: Volume 78, No. 4 (2012)

FUZZY SUBGROUPS COMPUTATION OF
FINITE GROUP BY USING THEIR LATTICES

Raden Sulaiman
$^1$Department of Mathematics
Faculty of Mathematics and Sciences
Universitas Negeri Surabaya
Surabaya, 60231, INDONESIA


Abstract. This paper gives a method to determine the number of fuzzy subgroups of finite group $G$ using diagram of lattice subgroups of $G$. This method can be used for abelian and non-abelian groups. First, an equivalence relation on the set of all fuzzy subgroups of group $G$ is defined. Second, this paper derive some theorems for determination of the number of fuzzy subgroups associated with some chains on the lattice subgroups of $G$. Then the demonstration of the method is given by determining the number of fuzzy subgroups of some finite group $G$.

Received: August 25, 2011

AMS Subject Classification: 06B05, 20N25, 01-08

Key Words and Phrases: equivalence, lattice, chain, fuzzy subgroup

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 4