# Characterizations and properties of bounded $L$-fuzzy sets

Document Type : Research Paper

Author

School of Science, Nanjing University of Posts and Telecommuni- cations, Nanjing 210023, China

Abstract

In 1997, Fang proposed the concept of boundedness of $L$-fuzzy sets
in $L$-topological vector spaces. Since then, this concept has been
widely accepted and adopted in the literature. In this paper,
several characterizations of bounded $L$-fuzzy sets in
$L$-topological vector spaces are obtained and some properties of
bounded $L$-fuzzy sets are investigated.

Keywords

#### References

\bibitem{DP}
D. Dubois and H. Prade, {\it Fuzzy sets and systems: theory and
applications}, Academic Press, New York, 1980.

\bibitem{F}
J. X. Fang, {\it The continuity of fuzzy linear order-homomorphism},
J. Fuzzy Math., {\bf 5}\textbf{(4)} (1997), 829--838.

\bibitem{FY}
J. X. Fang and C. H. Yan, {\it $L$-fuzzy topological vector spaces},
J. Fuzzy Math., {\bf 5}\textbf{(1)} (1997), 133--144.

\bibitem{HR}
U. H\"{o}hle and S. E. Rodabaugh, eds., {\it Mathematics of fuzzy
sets: logic, topology and measure theory, the handbooks of fuzzy
sets series, vol. 3}, Kluwer Academic Publishers, Dordrecht, 1999.

\bibitem{K}
A. K. Katsaras, {\it Fuzzy topological vector spaces I},  Fuzzy Sets
and Systems, {\bf 6} (1981), 85--95.

\bibitem{LL}
Y. M. Liu and M. K. Luo, {\it Fuzzy topology}, World Scientific
Publishing, Singapore, 1997.

\bibitem{W}
G. J. Wang,  {\it Theory of $L$-fuzzy topological spaces}, Shaanxi
Normal University Press, Xi'an, (in Chinese), 1988.

\bibitem{XF}
X. L. Xu and J. X. Fang, {\it Product spaces and quotient spaces of
$L$-fuzzy topological vector spaces}, In: Fuzzy Sets Theory and
Applications, Hebei University Press, Baoding, (in
Chinese), (1998), 20--22.

\bibitem{YF1}
C. H. Yan and J. X. Fang, {\it Generalization of Kolmogoroff's
theorem to $L$-topological vector spaces}, Fuzzy Sets and Systems,
{\bf 125} (2002), 177--183.

\bibitem{YF2}
C. H. Yan and J. X. Fang, {\it Locally bounded $L$-topological
vector spaces}, Information Sciences, {\bf 159} (2004), 273--281.

\bibitem{ZF}
H. P. Zhang and J. X. Fang, {\it Generalized locally bounded
$L$-topological vector spaces}, Fuzzy Sets and Systems, {\bf
162} (2011), 53--63.