Abstract
In this chapter, we determine the number of fuzzy subgroups of certain finite Abelian groups with respect to a suitable equivalence relation. This is motivated by the realization that in a theoretical study of fuzzy groups, fuzzy subgroups are distinguished by their level sets and not by their images in [0, 1]. We first present some results on the equivalence of fuzzy subsets of a given set. The results of this chapter are mainly from [4, 9, 10, 11, 12].
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N. Mordeson, J., R. Bhutani, K., Rosenfeld, A. Equivalence of Fuzzy Subgroups of Finite Abelian Groups. In: Fuzzy Group Theory. Studies in Fuzziness and Soft Computing, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10936443_8
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DOI: https://doi.org/10.1007/10936443_8
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Publisher Name: Springer, Berlin, Heidelberg
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