Abstract
This paper introduces a special Galois connection combined with the wedge-below relation. Furthermore, by using this tool, it is shown that the category of M-fuzzifying betweenness spaces and the category of M-fuzzifying convex spaces are isomorphic and the category of arity-2 M-fuzzifying convex spaces can be embedded in the category of M-fuzzifying interval spaces as a reflective subcategory.
Get full access to this article
View all access options for this article.
References
1.
Maruyama
Y.
, Lattice-valued fuzzy convex geometry , RIMS Kokyuroku 164 (2009 ), 22 –37 .
2.
Li
E.Q.
and
Shi
F.G.
, Some properties of M -fuzzifying convexities induced by M -orders , Fuzzy Sets Syst 350 (2018 ), 41 –54 .
3.
Li
H.Y.
and
Wang
K.
, L -ordered neighborhood systems of stratified L -concave structuresJ Nonlinear Convex A 21 (12 ) (2020 ), 2783 –2793 .
4.
Jin
Q.
and
Li
L.Q.
, On the embedding of L -convex spaces in stratified L -convex spaces , SpringerPlus 5 (1 ) (2016 ), 1610 .
5.
Kumar
R.
and
Garg
V.K.
, Introduction to lattice theory , Oliver and Boyd, 1995.
6.
Pang
B.
, Convenient properties of stratified L -convergence tower spaces , Filomat 33 (2019 ), 4811 –4825 .
7.
Pang
B.
, Categorical properties of L -fuzzifying convergence spaces , Filomat 32 (11 ) (2018 ), 4021 –4036 .
8.
Pang
B.
, Bases and subbases in (L , M )-fuzzy convex spaces , Comput Appl Math 39 (2 ) (2020 ), 41 .
9.
Pang
B.
and
Shi
F.G.
, Subcategories of the category of L -convex spaces , Fuzzy Sets Syst 313 (2017 ), 61 –74 .
10.
Pang
B.
and
Shi
F.G.
, Strong inclusion orders between L -subsets and its applications in L -convex spaces , Quaest Math 41 (8 ) (2018 ), 1021 –1043 .
11.
Pang
B.
and
Shi
F.G.
, Fuzzy counterparts of hull operators and interval operators in the framework of L -convex spaces , Fuzzy Sets Syst 369 (2019 ), 20 –39 .
12.
Rosa
M.V.
, On fuzzy topology fuzzy convexity spaces and fuzzy local convexity , Fuzzy Sets Syst 62 (1994 ), 97 –100 .
13.
S̆ostak
A.P.
, On a fuzzy topological structure , Suppl Rend Circ Mat Palermo Ser II 11 (1985 ), 89 –103 .
14.
Shen
C.
,
Chen
F.H.
and
Shi
F.G.
, Derived operators on M -fuzzifying convex spaces , J Intell Fuzzy Syst 37 (2019 ), 2687 –2696 .
15.
Shen
C.
and
Shi
F.G.
, L -convex systems and the categorical isomorphism to Scott-hull operatorsIran J Fuzzy Syst 15 (2 ) (2018 ), 23 –40 .
16.
Shi
F.G.
, L -fuzzy relation and L -fuzzy subgroupJ Fuzzy Math 8 (2000 ), 491 –499 .
17.
Shi
F.G.
and
Li
E.Q.
, The restricted hull operator of M -fuzzifying convex structures , J Intell Fuzzy Syst 30 (2015 ), 409 –421 .
18.
Shi
F.G.
and
Pang
B.
, Categories isomorphic to the category of L -fuzzy closure system spaces , Iran J Fuzzy Syst 10 (5 ) (2013 ), 129 –148 .
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 (7 ) (2017 ), 3655 –3669 .
21.
Van De Vel
M.
, Theory of convex structures , North-Holland, Amsterdam, 1993.
22.
Xiu
Z.Y.
and
Pang
B.
, M -fuzzifying cotopological spaces and M -fuzzifying convex spaces as M -fuzzifying closure spacesJ Intell Fuzzy Syst 33 (2017 ), 613 –620 .
23.
Yao
W.
, An approach to fuzzy frames via fuzzy posets , Fuzzy Sets Syst 166 (2011 ), 75 –89 .
24.
Yao
W.
and
Shi
F.G.
, Bases axioms and circuits axioms for fuzzifying matroids , Fuzzy Sets Syst 161 (2010 ), 3155 –3165 .
25.
Wang
B.
,
Li
Q.
and
Xiu
Z.Y.
, A categorical approach to abstract convex spaces and interval spaces , Open Mathematics 17 (2019 ), 374 –384 .
26.
Wang
G.J.
, Theory of topological molecular lattices , Fuzzy Sets Syst 47 (1992 ), 351 –376 .
27.
Wang
K.
and
Shi
F.G.
, M -fuzzifying topological convex spacesIran J Fuzzy Syst 15 (2018 ), 159 –174 .
28.
Wang
L.
,
Wu
X.Y.
and
Xiu
Z.Y.
, A degree approach to relationship among fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies , Open Mathematics 17 (2019 ), 913 –928 .
29.
Wu
X.Y.
and
Li
E.Q.
, Category and subcategories of (L , M )-fuzzy convex spaces , Iran J Fuzzy Syst 16 (1 ) (2019 ), 173 –190 .
30.
Wu
X.Y.
,
Li
E.Q.
and
Bai
S.Z.
, Geometric properties of M -fuzzifying convex structures , J Intell Fuzzy Syst 32 (6 ) (2017 ), 4273 –4284 .
31.
Wu
X.Y.
and
Shi
F.G.
, M -fuzzifying Bryant-Webster spaces and M -fuzzifying join spacesJ Intell Fuzzy Syst 35 (2018 ), 1807 –1819 .
32.
Wu
X.Y.
and
Shi
F.G.
, L -concave bases and L -topologicalconcave spacesJ Intell Fuzzy Syst 35 (2018 ), 4731 –4743 .
33.
Xiu
Z.Y.
and
Shi
F.G.
, M -fuzzifying interval spacesIran J Fuzzy Syst 14 (1 ) (2017 ), 145 –162 .
34.
Xiu
Z.Y.
, Convergence structures in L -concave spaces , J Nonlinear Convex A 21 (12 ) (2020 ), 2693 –2703 .
35.
Xiu
Z.Y.
and
Li
Q.H.
, Degrees of L -continuity for mappings between L -topological spaces , Mathematics 7 (11 ) (2019 ), 1013 –1028 .
36.
Xiu
Z.Y.
,
Li
Q.H.
and
Pang
B.
, Fuzzy convergence structures in the framework of L -convex spaces , Iran J Fuzzy Syst 17 (4 ) (2020 ), 139 –150 .
37.
Xiu
Z.Y.
,
Li
L.
and
Zhu
Y.
, A degree approach to special mappings between (L , M )-fuzzy convex spaces , J Nonlinear Convex A 21 (12 ) (2020 ), 2625 –2635 .
38.
Ying
M.S.
, A new approach for fuzzy topology , Fuzzy Sets Syst 39 (1991 ), 303 –321 .
39.
Zhong
Y.
and
Shi
F.G.
, Stratified (L , M )-fuzzy derived spaces , Iran J Fuzzy Syst 15 (2018 ), 109 –127 .