On the integrable noncompact fuzzy number space

Degang Chen; Xiao Ping Xue; Liangkuan Zhu

doi:10.1016/j.aml.2007.12.024

On the integrable noncompact fuzzy number space

Degang Chen^*
, Xiao Ping Xue
, Liangkuan Zhu

^*Corresponding author for this work

School of Mathematics

North China Electric Power University
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 over(E, ̂) that makes the existing fuzzy number space E¹ as its subspace. With a metric d¹, (over(E, ̂), d¹) is proven to be complete and separable and is the completed space of E¹ with respect to the metric d¹. It is also proven that over(E, ̂) can be embedded into a concrete Banach space L (0, 1] × L (0, 1] isometrically and isomorphically.

Original language	English
Pages (from-to)	1260-1266
Number of pages	7
Journal	Applied Mathematics Letters
Volume	21
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2007.12.024
State	Published - Dec 2008

Keywords

Embedding operator
Fuzzy number
Integrable noncompact fuzzy number

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10.1016/j.aml.2007.12.024

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N2 - 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 over(E, ̂) that makes the existing fuzzy number space E1 as its subspace. With a metric d1, (over(E, ̂), d1) is proven to be complete and separable and is the completed space of E1 with respect to the metric d1. It is also proven that over(E, ̂) can be embedded into a concrete Banach space L (0, 1] × L (0, 1] isometrically and isomorphically.

AB - 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 over(E, ̂) that makes the existing fuzzy number space E1 as its subspace. With a metric d1, (over(E, ̂), d1) is proven to be complete and separable and is the completed space of E1 with respect to the metric d1. It is also proven that over(E, ̂) can be embedded into a concrete Banach space L (0, 1] × L (0, 1] isometrically and isomorphically.

KW - Embedding operator

KW - Fuzzy number

KW - Integrable noncompact fuzzy number

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JF - Applied Mathematics Letters

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ER -

On the integrable noncompact fuzzy number space

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Keywords

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