The aim of this paper is to introduce and study the notions of (L, M)-double fuzzy topological molecular lattice, (L, M)-double fuzzy remote neighborhood space, and to construct the category (L, M)-DFRN which contains (L, M)-TDFRN as a full subcategory. (L, M)-TDFRN is shown as an isomorphic with (L, M)-DFTML. Finally, the notion of (L, M)-double fuzzy ideal was introduced and the theory of (L, M)-double fuzzy ideal convergence in an (L, M)-double fuzzy topological molecular lattice was established.
AbbasS.E. and Abd-AllahA.A., Lattice valued double syntopogenous structures, Journal of the Association of Arab Universites for Basic and Applied Sciences10 (2011), 33–41.
AdámekJ., HerrlichH. and StreckerG.E., Abstract and Concrete Categories, Wiley, New York, 1990.
4.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986), 87–96.
5.
AtanassovK., New operator defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems61 (1993), 131–142.
6.
ÇetkinV. and AygünH., Lattice valued double fuzzy preproximity spaces, Computers and Mathematics with Applications60 (2010), 849–864.
7.
ÇetkinV. and AygünH., On (L, M)-double fuzzy ideals, International Journal of Fuzzy Systems14(1) (2012), 166–174.
8.
ÇetkinV. and AygünH., On double fuzzy preuniformity, J Nonlinear Sci Appl6 (2013), 263–278.
9.
ChangC.L., Fuzzy topological spaces, Journal of Mathematical Analysis and Applications24 (1968), 182–190.
10.
ChenS.L., θ-convergence theory of ideals on completely distributive lattices, J Math13(2) (1993), 163–168.
11.
ChenS.L. and ChengJ.S., Theory of R-convergence of ideals on fuzzy lattices and its application, Korea, pp, Proceedings of the Fifth IFSA World Congress I (1993), 269–271.
12.
ChenS.L. and WuZ.X., Urysohn separation property in topological molecular lattices, Fuzzy Sets and Systems123 (2001), 177–184.
13.
ChenY., Convergence in topological molecular lattices, Fuzzy Sets and Systems84 (1996), 97–102.
14.
ÇokerD., An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces, Journal of Fuzzy Mathematics4 (1996), 749–764.
15.
ÇokerD. and DemirciM., An introduction to intuitionistic fuzzy topological spaces in Šostak’s sense, Busefal67 (1996), 67–76.
16.
GarciaJ.G. and RodabaughS.E., Order-theoretic, topological, categorical redundancides of interval-valued sets, grey sets, vague sets, interval-valued “intuitionistic” sets, “intuitionistic” fuzzy sets and topologies, Fuzzy Sets and Systems156 (2005), 445–484.
YueY. and FangJ., Categories isomorphic to the KubiakŠostak extension of TML, Fuzzy Sets and Systems157 (2006), 832–842.
39.
YueY. and FangJ., Fuzzy ideals and fuzzy limit structures, Iranian Journal of Fuzzy Systems5(1) (2008), 55–64.
40.
ZahranA.M., Azab Abd-AllahM., El-SaadyK. and GhareebA., The category of double preproximity spaces, Computers and Mathematics with Applications58 (2009), 1558–1572.
