In this paper, by means of implication operator → in a completely distributive lattice M, we define degrees of (L, M)-fuzzy convex structures, (L, M)-fuzzy closure systems and (L, M)-fuzzy Alexandrov topologies. Moreover, We discuss some properties of the degree of (L, M)-fuzzy convex spaces, the relations between the degree of (L, M)-fuzzy convex structures and the degree of (L, M)-fuzzy closure systems, and the relations between the degree of (L, M)-fuzzy convex structures and the degree of (L, M)-fuzzy Alexandrov topologies.
C.L.Chang, Fuzzy topological spaces, J Math Anal Appl24 (1968), 182–190.
2.
P.Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings)85 (1982), 403–414.
G.Gierz, K.H.Hofmann, K.Keimel, J.D.Lawson, M.Mislowe and D.S.Scott, Continuous Lattices and Domains,Cambridge University Press, Cambridge, 2003.
6.
U.Hohle and S.E.Rodabaugh, (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999.
7.
U.Hohle and A.Sostak, Axiomatic foundations of variablebasis fuzzy topology, in:
U.Hohle and
S.E.Rodabaugh(Eds.), Mathematics of Fuzzy Sets: Logic Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, pp. 123–272.
8.
Q.Jin and L.Q.Li, On the embedding of L-convex spaces in stratified L-convex spaces, Springer Plus5 (2016), 1610.
9.
T.Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mick- iewicz, Poznan, Poland, 1985.
10.
L.Q.Li and Q.Jin, p-Topologicalness and p-Regularity for lattice-valued convergence spaces, Fuzzy Sets Syst238 (2014), 26–45.
11.
L.Q.Li, Q.Jin and K.Hu, On stratified L-convergence spaces: Fischer's diagonal axiom, Fuzzy Sets Syst267 (2015), 31–40.
12.
L.Q.Li, On the category of enriched (L, M)-convex spaces, J Intell Fuzzy Syst33 (2017), 3209–3216.
13.
L.Q.Li, Q.Jin and K.Hu, Lattice-valued convergence associated with CNS spaces, Fuzzy Sets Syst (2018). DOI: 10.1016/j.fss.2018.05.023
14.
L.Q.Li, Q.Jin, K.Hu and F.F.Zhao, The axiomatic characterizations on L-fuzzy covering-based approximation operators, International Journal of General Systems46 (2017), 332–353.
15.
M.Lassak, On metric B-convexity for which diameters of any set and its hull are equal, Bull Acad Polon Sci25 (1977), 969–975.
B.Pang and F.G.Shi, Subcategories of the category of L- convex spaces, Fuzzy Sets Syst313 (2017), 61–74.
21.
B.Pang and Y.Zhao, Characterizations of L-convex spaces, Iran J Fuzzy Syst13(4) (2016), 51–61.
22.
B.Pang, Y.Zhao and Z.Y.Xiu, A new definition of order relation for the introduction of algebraic fuzzy closure operators, IntJ Approx Reason92 (2018), 87–96.
23.
B.Pang and Z.Y.Xiu, Lattice-valued interval operators and its induced lattice-valued convex structures, IEEE T Fuzzy Syst26(3) (2018), 1525–1534.
24.
B.Pang and F.-G.Shi, Strong inclusion orders between L-subsets and its applications in L-convex spaces, Quaest Math41(8) (2018), 1021–1043.
25.
B.Pang and F.-G.Shi, Fuzzy counterparts of hull spaces and interval spaces in the framework of L-convex spaces, Fuzzy Sets Syst (2018). DOI: 10.1016/j.fss.2018.05.012
26.
B.Pang and Z.-Y.Xiu, An axiomatic approach to bases and subbases in L-convex spaces and their applications, Fuzzy Sets Syst (2018). DOI: 10.1016/j.fss.2018.08.002
27.
C.Shen and F.G.Shi, L-convex systems and the categorical isomorphismto Scott-hull operators, Iran J Fuzzy Syst15(2) (2018), 23–40.
28.
M.V.Rosa, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst62 (1994), 97–100.
29.
V.P.Soltan, d-convexity in graphs, Soviet Math Dokl28 (1983), 419–421.
30.
X.Y.Wu, B.Davvaz and S.Z.Bai, On M-fuzzifying convex matroids and M-fuzzifying independent structures, J Intell Fuzzy Syst33(1) (2017), 269–280.
31.
F.G.Shi and E.Q.Li, The restricted hull operator of M- fuzzifying convex structures, J Intell Fuzzy Syst30 (2015), 409–421.
32.
F.G.Shi and Z.Y.Xiu, A new approach to the fuzzification of convex structures, Journal of Applied Mathematics2014, Article ID 249183.
