Abstract: Let E be an n-dimensioal Euclidean space, T the induced fuzzy topology for E[8], and λ and μ fuzzy sets in E. In[10], where L. Zadeh introduced the notion of the shadow of fuzzy set λ on a hyperplane H (denoted by S_H(λ)), the following statement was given:If λ and μ be fuzzy convex sets E and S_H(λ)=S_H(μ) for all hyperplanes H, then λ=μ.