Homeomorphism Problems of Fuzzy Real Number Space and The Space of Bounded Functions with Same Monotonicity on [-1,1]

  • Hua -Dong Wang
  • Si -Cong Guo
  • Seyed Mojtaba Hosseini Bamakan
  • Yong Shi

Abstract

In this paper, based on the fuzzy structured element, we prove that there is a bijection function between the fuzzy number space ε1 and the space B[−1, 1], which defined as a set of standard monotonic bounded functions with monotonicity on interval [−1, 1]. Furthermore, a new approach based upon the monotonic bounded functions has been proposed to create fuzzy numbers and represent them by suing fuzzy structured element. In order to make two different metrics based space in B[−1, 1], Hausdorff metric and Lp metric, which both are classical functional metrics, are adopted and their topological properties are discussed. In addition, by the means of introducing fuzzy functional to space B[−1, 1], we present two new fuzzy number’s metrics. Finally, according to the proof of homeomorphism between fuzzy number space ε1 and the space B[−1, 1], it’s argued that not only does it give a new way to study the fuzzy analysis theory, but also makes the study of fuzzy number space easier.

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Published
2015-10-03
How to Cite
WANG, Hua -Dong et al. Homeomorphism Problems of Fuzzy Real Number Space and The Space of Bounded Functions with Same Monotonicity on [-1,1]. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 10, n. 6, p. 129-143, oct. 2015. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/2079>. Date accessed: 16 july 2020. doi: https://doi.org/10.15837/ijccc.2015.6.2079.

Keywords

fuzzy numbers; fuzzy structured element, standard monotonic bounded functions, fuzzy functional, homeomorphism