The endograph metric plays an important role in fuzzy number theory. The endograph metric on the fuzzy number space E^1 is known to be separable but not complete. This paper deals with the completion of E^1 with respect to the endograph metric. It is shown that the space of all non-compact fuzzy number space F^*(R) is the completion of E^1 with respect to the endograph metric. It is proved that the endograph metric is approximative with respect to order on fuzzy number spaces F^*(R), also, the endograph metric is computable. Finally some analytic theorems are given with respect to the endograph metric.
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