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On an equivalence of fuzzy subgroups. II. (English) Zbl 1019.20033
Summary: This paper forms a sequel to part I [ibid. 123, No. 2, 259-264 (2001; Zbl 1009.20080)]. Here we determine the number of distinct equivalence classes of fuzzy subgroups of $G=\bbfZ_{p_1}+\cdots+\bbfZ_{p_n}$ where $p_1,p_2,\dots,p_n$ are distinct primes. We introduce the notion of a keychain of a chain of length $n+1$ and index of a keychain in order to determine the number of fuzzy subgroups of $G$. We achieve this by using induction on the index of a keychain.

20N25Fuzzy groups
20K01Finite abelian groups
03E72Fuzzy set theory
Full Text: DOI
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