STRATIFIED (L, M)-FUZZY DERIVED SPACES

Document Type: Research Paper

Authors

1 College of Science, North China University of Technology, Beijing, P. R. China and School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P. R. China

2 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P. R. China and Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, P. R. China

Abstract

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.
What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,
the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic to the category of stratified $(L, M)$-fuzzy derived spaces.

Keywords


[1] Y. C. Bai, The N-derived operator in L-fuzzy topological spaces, Journal of Shaanxi Normal
University (Natural Science Edition), 18 (1990), 8{11.
[2] P. Dwinger, Characterizations of the complete homomorphic images of a completely distribu-
tive complete lattice I, Indag. Math. (Proc), 85 (1982), 403{414.
[3] R. Engelking, General Topology, Warszawa, 1977.
[4] J. M. Fang, Derived opeartor in L-fuzzy topological spaces, The Journal of Fuzzy Mathemat-
ics, 10 (2002), 735{746.
[5] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets and Systems, 157 (2006), 820{
831.
[6] G. Gierz, K. H. Hofmann and K. Keimel, A Compendium of Continuous Lattices, Springer,
Berlin, 1980.
[7] J. L. Kelley, General Topology, Springer, New York, 1955.
[8] T. Kubiak, On Fuzzy Topologies, PhD thesis, Adam Mickiewicz, Poznan, Poland, 1985.
[9] Y. Liu and M. Luo, Fuzzy Topology, World Scientifi c Publishing, Singapore, 1997.
[10] P. M. Pu, Y. M. Liu, Fuzzy topology. I. neighborhood structure of a fuzzy point and moore-
smith convergence, Journal of Mathematical Analysis and Applications, 76 (1980), 571{599.
[11] F. G. Shi, The fuzzy derived induced by the derived operator of ordinary set and fuzzy topology
induced by the fuzzy derived operator, Fuzzy Systems and Mathematics, 5 (1991), 32{37.
[12] F. G. Shi, L-fuzzy derived opeartor and L-fuzzy topology, Journal of Yantai Teachers Univer-
sity (Natural Science Edition), 10 (1994), 161{166.
[13] F. G. Shi, Theory of L -nested sets and L -nested sets and its applications, Fuzzy Systems
and Mathematics, 4 (1995), 65{72.
[14] F. G. Shi, L-fuzzy interiors and L-fuzzy closures, Fuzzy Sets and Systems, 160 (2009), 1218{
1232.
[15] F. G. Shi and B. Pang, Categories isomorphic to the category of L-fuzzy closure system
spaces, Iranian Journal of Fuzzy Systems, 10(5) (2013), 127{146.
[16] J. B. Shi and L. X. Xuan, Strong derived sets and strong derived operators in L-fuzzy topo-
logical spaces, Journal of Nanjing Normal University (Natural Science Edition), 19 (1996),
7{12.

[17] A. P. Sostak, Basic structures of fuzzy topology, Journal of Mathematical Sciences, 78 (1996),
662{701.
[18] G. J. Wang, Theory of L-Fuzzy Topological Spaces, Shaanxi Normal University Press, Xi'an,
(in Chinese), 1988.
[19] G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),
351{376.
[20] M. S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991),
303{321.
[21] W. Yao, Moore-Smith convergence in (L;M)-fuzzy topology, Fuzzy Sets and Systems, 190
(2012), 47{62.
[22] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.