We show that the membership function μ(x) of a fuzzy group Gsatisfies the equation μ(x)=σ(e,x), where σ(x,y) is a similarityrelation on G which is invariant under left-translation. We also showthat under some natural assumptions one can represent the elements x∈ G as 1-1, onto transformations P_x on a suitable universe Ω suchthat μ(x) equals the proportion of points in Ω which arefixed-points of P_x. These results provide a deeper insight on theimpact of group operation on the membership vales μ(x).
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