In this paper, a notion of modified ⊤-convergence spaces (initially defined by Fang and Yue in FSS, 2017) is given. Then the relationships between the modified ⊤-convergence spaces and types of lattice-valued convergence spaces are established.
FangJ.M. and YueY.L.
, T-diagonal conditions and Continuous extension theorem, Fuzzy Sets and Systems321 (2017), 73–89.
6.
FloresP.V.
, MohapatraR.N. and RichardsonG.
, Lattice-valued spaces: Fuzzy convergence, Fuzzy Sets and Systems157 (2006), 2706–2714.
7.
FloresP.V. and RichardsonG.
, Lattice-valued convergence: Diagonal axioms, Fuzzy Sets and Systems159 (2008), 2520–2528.
8.
GaoX.Y.
, PangB. and YangX.F.
, Extensional L-fuzzy Q-convergence structures, Journal of Intelligent and Fuzzy Systems31(3) (2016), 1701–1708.
9.
GierzG.
, HofmannK.H.
, KeimelK.
, LawsonJ.D.
, MisloveM.W.
, ScottD.S.Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003.
10.
GutiérrezJ.
, García, On stratified L-valued filters induced by T-filters, Fuzzy Sets and Systems157 (2006), 813–819.
11.
HöhleU.
, ŠostakA.Axiomatic foundations of fixed-basis fuzzy topology, HöhelU.
, RodabaughS.E.
(Eds.), Mathematics of Fuzzy Sets: Logic, Toology and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, pp. 123–273.
12.
HuK. and LiJ.Q.
, The entropy and similarity measure of interval valued intuitionistic fuzzy sets and their relationship, International Journal of Fuzzy Systems15(3) (2013), 279–288.
13.
JägerG.
, A category of L-fuzzy convergence spaces, Quaestiones Mathematicae24 (2001), 501–517.
14.
JägerG.
, Gähler’s neighbourhood condition for lattice-valued convergence spaces, Fuzzy Sets and Systems204 (2012), 27–39.
15.
JägerG.
, Stratified LMN-convergence tower spaces, Fuzzy Sets and Systems, Fuzzy Sets and Systems282 (2016), 62–73.
16.
JägerG.
, Connectedness and local connectedness for latticevalued convergence spaces, Fuzzy Sets and Systems300 (2016), 134–146.
17.
JinQ. and LiL.Q.
, One-axiom characterizations on lattice-valued closure (interior) operators, Journal of Intelligent and Fuzzy Systems31 (2016), 1679–1688.
18.
JinQ.
, LiL.Q.
, LvY.R.et al., Connectedness for lattice-valued subsets in lattice-valued convergence spaces, Quaestiones Mathematicae, 10.2989/16073606.2018.1441920
19.
JinQ.
, LiL.Q. and MengG.W.
, On the relationships between types of L-convergence spaces, Iranian Journal of Fuzzy Systems1 (2016), 93–103.
20.
LiL.Q.
, On the category of enriched (L, M)-convex spaces, Journal of Intelligent and Fuzzy Systems33 (2017), 3209–3216.
21.
LiL.Q. and JinQ.
, On adjunctions between Lim, S)-Top, and S)-Lim, Fuzzy Sets and Systems182 (2011), 66–78.
22.
LiL.Q. and JinQ.
, On stratified}-convergence spaces: Pretopological axioms and diagonal axioms, Fuzzy Sets and Systems204 (2012), 40–52.
23.
LiL.Q. and JinQ.
, p-Topologicalness and p-Regularity for latticevalued convergence spaces, Fuzzy Sets and Systems238 (2014), 26–45.
24.
LiL.Q.
, JinQ. and HuK.
, On stratified L-convergence spaces: ’s diagonal axiom, Fischer’s Fuzzy Sets and Systems267 (2015), 31–40.
25.
LiL.Q.,
JinQ. and HuK., Lattice-valued convergence associated with CNS spaces, Fuzzy Sets and Systems (2018), 10.1016/j.fss.2018.05.023
26.
LiL.Q.
, JinQ.
, HuK. and ZhaoF.F.
, The axiomatic characterizations on L-fuzzy covering-based approximation operators, International Journal of General Systems46 (2017), 332–353.
27.
LiL.Q.
, JinQ.
, MengG.W.et al.The lower and upper p-topological (p-regular) modifications for lattice-valued convergence spaces, Fuzzy Sets and Systems282 (2016), 47–61.
28.
LiL.Q. and LiQ.G.
, On enriched L-topologies: Base and subbase, Journal of Intelligent and Fuzzy Systems28 (2015), 2423–2432.
29.
LiL.Q. and LiQ.G.
, A new regularity (p-regularity) of stratified-generalized convergence spaces, Journal of Computational Analysis and Applications2 (2016), 307–318.
30.
OrpenD. and JägerG.
, Lattice-valued convergence spaces: Extending the lattices context, Fuzzy Sets and Systems190 (2012), 1–20.
31.
PangB. and ZhaoY.
, L-fuzzy N-convergence structures, Journal of Intelligent and Fuzzy Systems30(5) (2016), 3033–3043.
32.
PangB. and ZhaoY.
, Several types of enriched (L,M)-fuzzy convergence spaces, Fuzzy Sets and Systems321 (2017), 55–72.
33.
PreussG.
, Fundations of Topology, Kluwer Academic Publishers, London, 2002.
34.
QiuY. and FangJ.M.
, The category of all T-convergence spaces and its cartesian-closedness, Iranian Journal of Fuzzy Systems14(3) (2017), 121–138.
35.
ReidL. and RichardsonG.
, Connecting T and Lattice-Valued Convergences, Iranian Journal of Fuzzy Systems (in press).
36.
RosenthalK.I.
, Quantales and Their Applications, Longman Scientific & Technical, 1990.
37.
SunS.B.
, XiuZ.Y. and LiQ.L.
, On fuzzifying matroids: Dual matroids and spanning, Journal of Intelligent and Fuzzy Systems3 (2015), 1435–1440.
38.
YaoW.
, On many-valued stratified L-fuzzy convergence spaces, Fuzzy Sets and Systems159 (2008), 2503–2519.
39.
ZhangD.X.
, An enriched category approach to many valued topology, Fuzzy Sets and Systems158 (2007), 349–366.
40.
ZhangX.F.
, LiL.Q. and MengG.W.
, A modified uncertain entailment model, Journal of Intelligent and Fuzzy Systems27(1) (2014), 549–553.
41.
ZhaoF.F.
, JinQ. and LiL.Q.
, The axiomatic characterizations on L-generalized fuzzy neighborhood system-based approximation operators, International Journal of General Systems47(2) (2018), 155–173.