There are di erent notions of fuzzy uniform structures and of fuzzy proximities that have been introduced in the literature. In this paper we are interested in the fuzzy uniform structure U in the sense of Gahler et al. (1998) which is de ned as some fuzzy lter and we are also interested in the fuzzy proximity N in the sense of Gahler et al. (1998), called the fuzzy proximity of the internal type that is de ned by means of another notion of symmetry not depending on an order-reversing involution. Here, we introduce the -level uniform structure U and the -level proximity N of U and N, respectively. We show that there is one-to-one correspondence between a fuzzy uniform structure U and the family (U ) ∈L0 of uniform structures that fullfills certain conditions, is given by: U =U and U(U)=WA∈U ; A6u .We also show that the topologies TU and TN associated with U and N coincides with the -level topologies of the fuzzy topologies U and N associated to U and N, respectively, that is, TU =( U) and TN =( N) . Moreover, we assign for each fuzzy uniform structure U an associated fuzzy proximity of the internal type N U and hence we get the relation between the -levels of U and of N U which is given by: NU =(N U) . c
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