GRADUAL NORMED LINEAR SPACE

Document Type : Research Paper

Authors

Department of Mathematics, Sahand university of technology, Tabriz- Iran

Abstract

In this paper, the gradual real numbers are considered and the
notion of the gradual normed linear space is given. Also some topological
properties of such spaces are studied, and it is shown that the gradual normed
linear space is a locally convex space, in classical sense. So the results in locally
convex spaces can be translated in gradual normed linear spaces. Finally, we
give an example of a gradual normed linear space which is not normable in
classical analysis.

Keywords

References

[1] J. B. Conway,A course in functional analysis, Springer-Verlag, New York, 1990.
[2] D. Dubois and H. Prade,Gradual elements in a fuzzy set, Soft Computing-A Fusion of Foundations, Methodologies and Applications,12 (2007), 165-175.
[3] J. Fortin, D. Dubois and H. Prade,Gradual numbers and their application to fuzzy interval analysis, IEEE Transactions on Fuzzy Systems, 16 (2008), 388-402.
[4] U. Hoehle,Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic, Fuzzy Sets and Systems,24 (1987), 263-278.
[5] E. Kaucher,Interval analysis in the extended interval space R, Computing Supplement,2(1980), 33-49.
[6] R. Lowen,Fuzzy set theory, Ch. 5 : Fuzzy Real Numbers, Kluwer, Dordrecht, 1996.
[7] S. E. Rodabaugh,Fuzzy addition in the L-fuzzy real line, Fuzzy Sets and Systems, 8 (1982),39-51.
[8] I. Sadeqi and M. Salehi,Fuzzy compact operators and topological degree theory, Fuzzy Sets and Systems,160 (2009), 1277-1285.
Iranian Journal of Fuzzy Systems
Volume 8, Issue 5 - Serial Number 5
September and October 2011
Pages 131-139

Files

Share

How to cite

Statistics