Abstract
In this paper, the concept of compactness measures of (L, M)-fuzzy Q-convergence spaces is introduced. It is used to define compactness measures of (L, M)-fuzzy topological spaces and pointwise (L, M)-fuzzy quasi-uniform spaces. It is shown that the concept of compactness measures satisfies the lattice-valued Tychonoff theorem in the framework of (L, M)-fuzzy Q-convergence spaces and (L, M)-fuzzy topological spaces. Also, it is proved that the compactness measures of a pointwise (L, M)-fuzzy quasi-uniform space is equal to the compactness measures of its induced (L, M)-fuzzy topological space.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Eş
H.
and
Çoker
D.
, On several types of degree of fuzzy compactness , Fuzzy Sets Syst 87 (1997 ), 349 –359 .
2.
Fang
J.M.
, Categories isomorphic to L-FTOP , Fuzzy Sets Syst 157 (2006 ), 820 –831 .
3.
Gantner
T.E.
,
Steinlage
R.C.
and
Warren
R.H.
, Compactness in fuzzy topological spaces , J Math Anal Appl 62 (1978 ), 547 –562 .
4.
Jäger
G.
, A category of L-fuzzy convergence spaces , Quaest Math 24 (2001 ), 501 –517 .
5.
Jäger
G.
, Degrees of compactness in fuzzy convergence spaces , Fuzzy Sets Syst 125 (2002 ), 167 –175 .
6.
Jäger
G.
, Compactification of lattice-valued convergence spaces , Fuzzy Sets Syst 161 (2010 ), 1002 –1010 .
7.
Jäger
G.
, Compactness in lattice-valued function spaces , Fuzzy Sets Syst 161 (2010 ), 2962 –2974 .
8.
Jäger
G.
, A one-point compactification for lattice-valued convergence spaces , Fuzzy Sets Syst 190 (2012 ), 21 –31 .
9.
Jäger
G.
, Largest and smallest T2-compactifications of latticevalued convergence spaces , Fuzzy Sets Syst 190 (2012 ), 32 –46 .
10.
Kelley
J.L.
, General Topology , Springer-Verlag , New York , 1975 .
11.
Kubiak
T.
, On fuzzy topologies , Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985 .
12.
Li
H.Y.
,
Shi
F.G.
, Degrees of fuzzy compactness in L-fuzzy topological spaces , Fuzzy Sets Syst 161 (2010 ), 988 –1001 .
13.
Liu
Y.M.
, Compactness and Tychnoff theorem in fuzzy topological spaces , Acta Math Sin 24 (1981 ), 260 –268 .
14.
Pang
B.
and
Fang
J.M.
, L-fuzzy Q-convergence structures , Fuzzy Sets Syst 182 (2011 ), 53 –65 .
15.
Pang
B.
, Further study on L-fuzzy Q-convergence structures , Iran J Fuzzy Syst 10 (5 ) (2013 ), 149 –166 .
16.
Pang
B.
, On (L , M )-fuzzy convergence spaces , Fuzzy Sets Syst 238 (2014 ), 46 –70 .
17.
Pang
B.
and
Shi
F.G.
, Degrees of compactness of (L , M )-fuzzy convergence spaces and its applications , Fuzzy Sets Syst 251 (2014 ), 1 –22 .
18.
Pang
B.
, Enriched (L , M )-fuzzy convergence spaces , J Intell Fuzzy Syst 27 (2014 ), 93 –103 .
19.
Pang
B.
and
Zhao
Y.
, Stratified (L , M )-fuzzy Q-convergence spaces , Iran J Fuzzy Syst 13 (4 ) (2016 ), 95 –111 .
20.
Pang
B.
and
Zhao
Y.
, L-fuzzy N-convergence structures , J Intell Fuzzy Syst 30 (2016 ), 3033 –3043 .
21.
Pang
B.
and
Zhao
Y.
, Several types of enriched (L , M )-fuzzy convergence spaces , Fuzzy Sets Syst (2016 ). http://dx.doi.org/10.1016/j.fss.2016.09.001.
22.
Preuss
G.
, Foundations of Topology – An Approach to Convenient Topology , Kluwer Academic Publisher , Dordrecht, Boston, London , 2002 .
23.
Shi
F.G.
, Countable compactness and the Lindelöf property of L-fuzzy sets , Iran J Fuzzy Syst 1 (2004 ), 79 –88 .
24.
Shi
F.G.
, A new notion of fuzzy compactness inL-topological spaces , Inform Sci 173 (2005 ), 35 –48 .
25.
Shi
F.G.
, A new definition of fuzzy compactness , Fuzzy Sets Syst 158 (2007 ), 1486 –1495 .
26.
Šostak
A.P.
, On a fuzzy topological structure , Suppl Rend Circ Mat Palermo Ser II 11 (1985 ), 89 –103 .
27.
Yao
W.
, Moore-Smith convergence in (L , M )-fuzzy topology , Fuzzy Sets Syst 190 (2012 ), 47 –62 .
28.
Yue
Y.L.
and
Fang
J.M.
, Extension of Shi’s quasi-uniformities in a Kubiak-Šostak sense , Fuzzy Sets Syst 157 (2006 ), 1956 –1969 .
29.
Zhao
D.S.
, The N-compactness in L-fuzzy topological spaces , J Math Anal Appl 128 (1987 ), 64 –70 .