It is well-known that the space Eⁿ of fuzzy numbers (i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets) in the n-dimensional Euclidean space Rⁿ is separable but not complete with respect to the L_p-metric.
In this paper, we introduce the space F_p(Rⁿ) that is separable and complete with respect to the L_p-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing
convex condition.

Keywords: Fuzzy numbers,Compact sets,L_p-metric