On the number of fuzzy subgroups of symmetric group S5
Abstract
This article computes the number of fuzzy subgroups of symmetric group S5. First, an equivalence relation on the set of all fuzzy subgroups of a group G is defined.Without any equivalence relation on fuzzy subgroups of group G, the number of fuzzy subgroups is infinite, even for the trivial group. TheInclusion-Exclusion principle is used to determine the number of distinct fuzzy subgroups of symmetric group S5. Some inequalities satisfied by this number are also established for n ≥ 5.
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