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Zbl 0757.46066
Wu, Congxin; Ma, Ming
Embedding problem of fuzzy number space. I.
(English)
[J] Fuzzy Sets Syst. 44, No.1, 33-38 (1991). ISSN 0165-0114

Summary: Using a theorem of {\it R. Goetschel} and {\it W. Voxman} [ibid. 18, 31- 43 (1986; Zbl 0626.26014)] we can embed fuzzy number space $E\sp 1$ into a concrete Banach space $\overline{C}[0,1]\times\overline{C}[0,1]$. In addition, using a Rådström embedding theorem, {\it M. L. Puri} and {\it D. A. Ralescu} [J. Math. Anal. Appl. 91, 552-558 (1983; Zbl 0528.54009)] embed $E\sp 1$ into a normed space $X$ with $X=C-C$. In fact, $\overline{X}$, the completion of $X$, is isometrically isomorphic to $\overline{C}[0,1]\times\overline{C}[0,1]$.
MSC 2000:
*46S40 Fuzzy functional analysis
03E72 Fuzzy sets (logic)
54A40 Fuzzy topology

Keywords: isometrical isomorphism; fuzzy number space; concrete Banach space; Rådström embedding theorem

Citations: Zbl 0626.26014; Zbl 0528.54009

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