Different from the separation axioms in the framework of (L, M)-fuzzy convex spaces defined by Liang et al.(2019). In this paper, we give some new investigations on separation axioms in (L, M)-fuzzy convex structures by L-fuzzy hull operators and r-L-fuzzy biconvex. We introduce the concepts of r-LFSi spaces where i = {0, 1, 2, 3, 4}, and obtain various properties. In particular, we discuss the invariance of these separation properties under subspace and product.
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References
1.
ChepoiV., Separation of two convex sets in convexity structures, J Geom50 (1994), 30–51.
2.
EckhoffJ., Radon’s theorem in convex product structures I, Monatsh Math72 (1968), 303–314.
3.
EckhoffJ., Radon’s theorem in convex product structures II, Monatsh Math73 (1969), 17–30.
4.
EllisE., A general set-separation theorem, Duke Math J19 (1952), 417–421.
5.
GoguenJ.A., L-fuzzy sets, J Math Anal Appl18 (1967), 145–174.
6.
GottwaldS., Fuzzy points and local properties of fuzzy topological spaces, Fuzzy Sets and Systems5 (1981), 199–201.
7.
HazraR.N., SamantaS.K. and ChattopadhyayK.C., Fuzzy topology redefined, Fuzzy Sets and Systems45 (1992), 79–82.
8.
JamisonR.E., A general theory of convrxity, Dissertation, University of Washington, Seattle, Washington, (1974).
9.
KayD.C. and WombleE.W., Axiomatic convexity theory and the relationship between the Caratheodory, Helly and Radon numbers, Pacific J Math38 (1971), 471–485.
10.
LassakM., On metric B-convexity for which diameters of any set and its hull are equal, Bull Acad Polon Sci Ser Sci Math Astronom Phys25 (1977), 969–975.
11.
LiE. and ShiF.-G., Some properties of M-fuzzifying convexities induced by M-orders, Fuzzy Sets and Systems350 (2018), 41–54.
12.
LiangC.-Y., LiF.-H. and ZhangJ., Separation axioms in (L, M)- fuzzy convex spaces, Journal of Intelligent and Fuzzy Systems36 (2019), 3649–3660.
PangB. and ShiF.-G., Subcategories of the category of L-convex spaces, Fuzzy Sets and Systems313 (2017), 61–74.
15.
PangB. and ShiF.-G., Fuzzy counterparts of hull operators and interval operators in the framework of L-convex spaces, Fuzzy Sets and Systems369 (2019), 20–39.
16.
PangB. and ShiF.-G., Strong inclusion orders between L-subsets and its applications in L-convex spaces, Quaestiones Mathematicae41(8) (2018), 1021–1043.
17.
PangB. and XiuZ.-Y., An axiomatic approach to bases and subbases in L-convex spaces and their applications, Fuzzy Sets and Systems (2018). DOI:10.1016/j.fss.2018.08.002
18.
PuP.-M. and LiuY.-M., Fuzzy topology, Part I-Neighborhood structure of a fuzzy point and Moore-Smith convergence, J Math Anal Appl76 (1980), 571–5994.
19.
RodabaughS.E., Powerset operator based foundation for point-set latticetheoretic (poslat) fuzzy set theories and topologies, Quaest Math20(3) (1997), 463–530.
20.
RosaM.V., A study of fuzzy convexity with special reference to separation properties, Ph.D. Thesis, Cochin University of Science and Technology, Kerala, India, (1994).
21.
RosaM.V., On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets and Systems62 (1994), 97–100.
22.
SayedO.R., El-SanousyE. and RaghpY.H., Sayed, On (L,M)- fuzzy convex structures, Filomat33(13) (2019), 4151–4163.
23.
ShenC. and ShiF.-G., Characteriztions of L-convex spaces via domain theory, Fuzzy Sets and Systems (2019). DOI:10.1016/j.fss.2019.02.009
