Stratified $(L,M)$-fuzzy Q-convergence spaces

Document Type: Research Paper


Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China


This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $(L,M)$-fuzzy topological spaces can be embedded in the category of stratified $(L,M)$-fuzzy Q-convergence spaces as a reflective subcategory, and the former is isomorphic to the category of topological stratified $(L,M)$-fuzzy Q-convergence spaces.


[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New
York, 1990.
[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
[3] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets Syst., 157 (2006), 820{831.
[4] J. M. Fang, Strati ed L-ordered convergence structures, Fuzzy Sets Syst., 161 (2010), 2130{
[5] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies,
Fuzzy Sets Syst., 161 (2010), 2923{2944.
[6] M. Guloglu and D. Coker, Convergence in I-fuzzy topological spaces, Fuzzy Sets Syst., 151
(2005), 615{623.
[7] U. Hohle and A. P. Sostak, Axiomatic foudations of xed-basis fuzzy topology, In: U. Hohle,
S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory,
Handbook Series, vol.3, Kluwer Academic Publishers, Boston, Dordrecht, London, (1999),
[8] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501{517.
[9] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst., 156 (2005),
[10] G. Jager, Pretopological and topological lattice-valued convergence spaces, Fuzzy Sets Syst.,
158 (2007), 424{435.
[11] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets Syst., 159 (2008),
[12] G. Jager, Fischer's diagonal condition for lattice-valued convergence spaces, Quaest. Math.,
31 (2008), 11{25.
[13] G. Jager, Strati ed LMN-convergence tower spaces, Fuzzy Sets Syst., 282 (2016), 62{73.
[14] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
[15] L. Q. Li and Q. Jin, On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets Syst.,
182 (2011), 66{78.
[16] L. Q. Li and Q. Jin, On strati ed L-convergence spaces: Pretopological axioms and diagonal
axioms, Fuzzy Sets Syst., 204 (2012), 40{52.
[17] R. Lowen, Convergence in fuzzy topological spaces, Gen. Topl. Appl., 10 (1979),147{160.
[18] K. C. Min, Fuzzy limit spaces, Fuzzy Sets Syst., 32 (1989), 343{357.
[19] B. Pang and J.M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011),
[20] B. Pang, Futher study on L-fuzzy Q-convergence structures, Iranian Journal of Fuzzy Systems,
10(5) (2013), 147{164.
[21] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70.
[22] B. Pang and F. G. Shi, Degrees of compactness of (L;M)-fuzzy convergence spaces and its
applications, Fuzzy Sets Syst., 251 (2014), 1{22.
[23] B. Pang, Enriched (L;M)-fuzzy convergence spaces, J. Intell. Fuzzy Syst., 27 (2014), 93{103.
[24] G. Preuss, Foundations of topology{an approach to convenient topology, Kluwer Academic
Publisher, Dordrecht, Boston, London, 2002.
[25] A. P. Sostak, On a fuzzy topological structure, Suppl. Rend. Circ. Mat. Palermo Ser. II, 11
(1985), 89{103.
[26] L. S. Xu, Characterizations of fuzzifying topologies by some limit structures, Fuzzy Sets Syst.,
123 (2001), 169{176.
[27] W. Yao, On many-valued strati ed L-fuzzy convergence spaces, Fuzzy Sets Syst., 159 (2008),
[28] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),
[29] W. Yao, Moore-Smith convergence in (L;M)-fuzzy topology, Fuzzy Sets Syst., 190 (2012),