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On the integrable noncompact fuzzy number space

✍ Scribed by Degang Chen; XiaoPing Xue; Liangkuan Zhu

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 232 KB
Volume: 21
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2007.12.024

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✦ Synopsis

In this paper an extension of the existing fuzzy number, called integrable noncompact fuzzy number, is proposed. The representation theorems of integrable noncompact fuzzy number by intervals and functions are also presented. All the integrable noncompact fuzzy numbers form an integrable noncompact fuzzy number space Ê that makes the existing fuzzy number space E 1 as its subspace. With a metric d 1 , ( Ê, d 1 ) is proven to be complete and separable and is the completed space of E 1 with respect to the metric d 1 . It is also proven that Ê can be embedded into a concrete Banach space L(0, 1] × L(0, 1] isometrically and isomorphically.

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