A NEW NOTION OF FUZZY PS-COMPACTNESS

Document Type: Research Paper

Author

Department of Mathematics, Wuyi University, Guangdong 529020, P.R.China

Abstract

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

Keywords


[1] S. Z. Bai,Pre-semiclosed sets and PS-convergence in L-fuzzy topological spaces, J. Fuzzy

Math.,9 (2001), 497-509.

[2] S. Z. Bai,L-fuzzy PS-compactness, International Journal of Uncertainty, Fuzziness and

Knowledge-Based Systems,10 (2002), 201-209.

[3] S. Z. Bai,Near PS-compact L-subsets, Information Sciences, 115 (2003), 111-118.

[4] C. L. Chang,Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.

[5] P. Dwinger,Characterizations of the complete homomorphic images of a completely distributive

complete lattice, I, Nederl. Akad. Wetensch. Indag. Math., 44 (1982), 403-414.

[6] G. Gierz and et al.,A Compendium of Continuous Lattices, Springer Verlag, Berlin, 1980.

[7] Y. M. Liu and M. K. Luo,Fuzzy topology, World Scientific Publishing, Singapore, 1998.

[8] F. G. Shi,Countable compactness and the Lindel¨of propeerty of L-fuzzy sets, Iranian Journal

of Fuzzy Systems,1 (2004), 79-88.

[9] F. G. Shi,Semicompactness in L-topological spaces, International Journal of Mathematics

Mathematical Sciences,12 (2005), 1869-1878.

[10] F. G. Shi,A new definition of fuzzy compactness, Fuzzy Sets and Systems, 158 (2007),

1486-1495.

[11] G. J. Wang,Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.