Sage Journals: Discover world-class research

Abstract

In fuzzy set theory, fuzzy convex structures are important mathematical structures. In this paper, we focus on separation axioms in fuzzy convex spaces. Concretely, we introduce S₀, S₁ and S₂ separation axioms in fuzzy convex spaces and establish their relationships. Furthermore, we investigate their hereditary and productive properties.

Keywords

Fuzzy convex structures separation axioms

Get full access to this article

View all access options for this article.

References

Chang

C.L.

, Fuzzy topological spaces, J Math Anal Appl 24 (1968), 182–193.

Eills

J.W.

, A general set-separation theorem, Duke Math J 19 (1952), 417–421.

Jamison

R.E.

, A General Theory of Convexity, Dissertation, University of Washington, seattle, Washington, (1974).

Kubiak

, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, (1985).

Liang

C.-Y.

and Li

F.-H.

, A degree approach to separation axioms in M-fuzzifying convex spaces, J Intell Fuzzy Syst 36 (2019), 2885–2893.

Q.-H.

, Huang

H.-L.

and Xiu

Z.-Y.

, Degrees of special mappings in the theory of L-convex spaces, J Intell Fuzzy Syst 37 (2019), 2265–2274.

Maruyama

, Lattice-valued fuzzy convex geometry, RIMS Kokyuroku 1641 (2009), 22–37.

Pang

, Categorical properties of-fuzzifying convergence spaces, Filomat 32 (2018), 4021–4036.

Pang

, Convenient properties of stratified L-convergence tower spaces, Filomat 33 (2019), 4811–4825.

10.

Pang

, Hull operators and interval operators in the (L, M)-fuzzy convex spaces, Fuzzy Sets Syst (2019). DOI:10.1016/j.fss.2019.11.010

11.

Pang

, Bases and subbases in (L, M)-fuzzy convex spaces, Comput Appl Math (2020), 39–41.

12.

Pang

and Shi

F.-G.

, Subcategories of the category of L-convex spaces, Fuzzy Sets Syst 313 (2017), 61–74.

13.

Pang

and Shi

F.-G.

, Fuzzy counterparts of hull spaces and interval spaces in the framework of L-convex spaces, Fuzzy Sets Syst 369 (2019), 20–39.

14.

Pang

and Xiu

Z.-Y.

, Lattice-valued interval operators and its induced lattice-valued convex structures, IEEE Trans Fuzzy Syst 26 (2018), 1525–1534.

15.

Pang

and Xiu

Z.-Y.

, An axiomatic approach to bases and subbases in L-convex spaces and their applications, Fuzzy Sets Syst 369 (2019), 40–56.

16.

Rosa

M.V.

, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity, Fuzzy Sets Syst 62 (1994), 97–100.

17.

Shen

and Shi

F.-G.

, Characterizations of L-convex spaces via domain theory, Fuzzy Sets Syst 380 (2020), 44–63.

18.

Shi

F.-G.

and Li

E.-Q.

, The restricted hull operator of M-fuzzifying convex structures, J Intell Fuzzy Syst 30 (2016), 409–421.

19.

Shi

F.-G.

and Xiu

Z.-Y.

, A new approach to the fuzzification of convex structures, J Appl Math 2014 (2014), 1–12.

20.

Shi

F.-G.

and Xiu

Z.-Y.

, (L, M)-fuzzy convex structures, J Nonlinear Sci Appl 10 (2017), 3655–3669.

21.

van de Vel

, Theory of convex structures, North-Holland, Amsterdam, (1993).

22.

Wang

, Li

Q.-H.

and Xiu

Z.-Y.

, A categorical approach to abstract convex spaces and interval spaces, Open Math 17 (2019), 374–384.

23.

Wang

and Shi

F.-G.

, Fuzzifying interval operators, fuzzifying convex structures and fuzzy pre-orders, Fuzzy Sets Syst (2019). DOI:10.1016/2019.04.022

24.

Wang

and Pang

, Coreflectivities of (L, M)-fuzzy convex structures and (L, M)-fuzzy cotopologies in (L, M)-fuzzy closure systems, J Intell Fuzzy Syst 37 (2019), 3751–3761.

25.

Wang

, Wu

X.-Y.

and Xiu

Z.-Y.

, A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies, Open Math 17 (2019), 913–928.

26.

X.-Y.

and Bai

S.-Z.

, Onconvex structures and M-fuzzifying Peano interval spaces, J Intell Fuzzy Syst 30 (2016), 2447–2458.

27.

X.-Y.

and Bai

S.-Z.

, M-fuzzifying gated amalgamations of M-fuzzifying geometric interval spaces, J Intell Fuzzy Syst 33 (2017), 4017–4029.

28.

X.-Y.

and Li

E.-Q.

, Category and subcategories of (L, M)-fuzzy convex spaces, Iran J Fuzzy Syst 16 (2019), 173–190.

29.

Xiu

Z.-Y.

, Li

Q.-H.

and Pang

, Fuzzy convergence structures in the framework of L-convex spaces, Iran J Fuzzy Syst (2020), 139–150.

30.

Xiu

Z.-Y.

and Pang

, M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces, J Intell Fuzzy Syst 33 (2017), 613–620.

31.

Xiu

Z.-Y.

and Pang

, A degree approach to special mappings between M-fuzzifying convex spaces, J Intell Fuzzy Syst 35 (2018), 705–716.

32.

Xiu

Z.-Y.

and Pang

, Base axioms and subbase axioms in M-fuzzifying convex spaces, Iran J Fuzzy Syst 15 (2018), 75–87.

33.

Xiu

Z.-Y.

and Shi

F.-G.

, M-fuzzifying interval spaces, Iran J Fuzzy Syst 14 (2017), 145–162.

34.

Yang

and Li

, A new approach to interval operators in L-convex spaces, Nonlinear Convex Anal, Accepted.

35.

Yang

and Shi

, L-biconvex sets on some fuzzy algebraic substructures, AIMS Math 5 (2020), 4311–4321.

Separation axioms in fuzzy convex spaces

Abstract

Keywords

Get full access to this article

References