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Embedding problem of fuzzy number space. I. (English) Zbl 0757.46066

Summary: Using a theorem of R. Goetschel and W. Voxman [ibid. 18, 31- 43 (1986; Zbl 0626.26014)] we can embed fuzzy number space \(E^ 1\) into a concrete Banach space \(\overline{C}[0,1]\times\overline{C}[0,1]\). In addition, using a Rådström embedding theorem, M. L. Puri and D. A. Ralescu [J. Math. Anal. Appl. 91, 552-558 (1983; Zbl 0528.54009)] embed \(E^ 1\) 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:

46S40 Fuzzy functional analysis
03E72 Theory of fuzzy sets, etc.
54A40 Fuzzy topology
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References:

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