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The sendograph metric on the space of fuzzy numbers is known to be separable, but not complete. This paper deals with the completion of the sendograph metric. The completion of fuzzy number space with respect to the sendograph metric is constructed. Also, a uniformly equivalent description of the sendograph metric is given which reveals the internal relation between the sendograph and endograph metrics.
The endograph metric plays an important role in fuzzy number theory. The endograph metric on the fuzzy number space E1 is known to be separable but not complete. This paper deals with the completion of E1 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 E1 with respect to the endograph metric. It is proved that the endograph...
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