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Embedding problem of fuzzy number space. I. (English) Zbl 0757.46066
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 $\overline{C}[0,1]\times\overline{C}[0,1]$.

46S40Fuzzy functional analysis
03E72Fuzzy set theory
54A40Fuzzy topology
Full Text: DOI
[1] Bergstrom, H.: Weak convergence of measures. (1982)
[2] Goetschel, R.; Voxman, W.: Elementary fuzzy calculus. Fuzzy sets and systems 18, 31-43 (1986) · Zbl 0626.26014
[3] Natanson, N.: Theory of real variables. (1950)
[4] Kaleva, O.: Fuzzy differential equations. Fuzzy sets and systems 24, 301-317 (1987) · Zbl 0646.34019
[5] Kaleva, O.: The Cauchy problem for fuzzy differential equations. Fuzzy sets and systems 35, 389-396 (1990) · Zbl 0696.34005
[6] Marłoka, M.: On fuzzy integrals. Proc. 2nd Polish symp. On interval and fuzzy mathematics (1987)
[7] Puri, M. L.; Ralescu, D. A.: Differentials for fuzzy functions. J. math. Anal. appl. 91, 552-558 (1983) · Zbl 0528.54009
[8] Puri, M. L.; Ralescu, D. A.: Fuzzy random variables. J. math. Anal. appl. 114, 409-422 (1986) · Zbl 0592.60004
[9] Rådström, H.: An embedding theorem for spaces of convex sets. Proc. amer. Math. soc. 3, 165-169 (1952) · Zbl 0046.33304
[10] Yosida, K.: Functional analysis. (1965) · Zbl 0126.11504