Elsevier

Fuzzy Sets and Systems

Volume 144, Issue 3, 16 June 2004, Pages 459-470
Fuzzy Sets and Systems

Counting the number of fuzzy subgroups of an abelian group of order pnqm

https://doi.org/10.1016/S0165-0114(03)00224-0Get rights and content

Abstract

In this paper, we determine the number of fuzzy subgroups of G=Zpn+Zqm where p,q are distinct primes, and n,m are any two natural numbers. First, we represent the number of maximal chains of G as a summation through m involving certain binomial coefficients. Using this concise expression, we propose a combinatorial formula for the number of fuzzy subgroups of G and verify it for specific values of m and n. Finally, we sketch a proof for the general case.

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