Abstract
Based on a completely distributive De Morgan algebra L, the notion of pointwise L-fuzzifying (quasi-)uniformity is introduced. It is shown that a pointwise L-fuzzifying quasi-uniformity can induce two L-fuzzifying topologies and , and the relations between and are investigated.
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References
1.
Gutierrez Garcia
J.
,
de PradaVicente
M.A.
and
Śosta
A.P.
, A unified approach to the concept of fuzzy (L, M)-uniform space , in:
Rodabaug
S.E.
and
Klemen
E.P.
(Eds.), Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic , vol. 20 , Kluwer Academic Publishers , Boston, Dordrecht, London , 2003 , pp. 81 –114 , (Chapter 3) .
2.
Höhle
U.
, Probabilistic metrization of fuzzy uniformities , Fuzzy Sets Syst 8 (1982 ), 63 –69 .
3.
Hutton
B.
, Uniformities on fuzzy topological spaces , J Math Anal Appl 58 (1977 ), 557 –571 .
4.
Kotzě
W.
, Uniform Spaces in:
Höhl
U.
and
Rodabaug
S.E.
(Eds.), Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory , Kluwer Academic Publishers , Boston, Dordrecht, London , 1999 , pp. 553 –580 , (Chapter 8) .
5.
Liu
Y.M.
, Pointwise characterizations of complete regularity and imbedding theorem in fuzzy topological space , Sci Sinica Ser (A) 8 (1982 ), 675 –682 .
6.
Liu
Y.M.
and
Luo
M.K.
, Fuzzy topology , World Scientific Publication , Singapore , 1998 .
7.
Lowen
R.
and
Xu
L.S.
, Alternative characterizations of FNCS , Fuzzy Sets and Systems 104 (3 ) (1999 ), 381 –391 .
8.
Pu
B.M.
and
Liu
Y.M.
, Fuzzy topology I, Neighborhood structure of fuzzy point and Moore-Smith convergence , J Math Anal Appl 76 (1980 ), 571 –579 .
9.
Rodabaugh
S.E.
, A theory of fuzzy uniformities with applications to the fuzzy real lines , J Math Anal Appl 129 (1988 ), 37 –70 .
10.
Shi
F.-G.
, Pointwise uniformities in fuzzy set theory , Fuzzy Sets Syst 98 (1998 ), 141 –146 .
11.
Shi
F.-G.
, Topologies in pointwise quasi-uniform molecular lattices , Fuzzy Syst Math 12 (1 ) (1998 ), 141 –146 . (in Chinese) .
12.
Wang
G.J.
, Theory of topological molecular lattices , Fuzzy Sets Syst 47 (3 ) (1992 ), 351 –376 .
13.
Wang
G.J.
and
Wu
H.
, Quasi-uniformities and topologies , Acta Math Sinica 2 (1993 ), 351 –376 .
14.
Xu
L.S.
, Characterizations of fuzzifying topologies by some limit structures , Fuzzy Sets Syst 123 (2001 ), 169 –176 .
15.
Ying
M.S.
, A new approach to fuzzy topology (I) , Fuzzy Sets Syst 39 (1991 ), 303 –321 .
16.
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 .
17.
Yue
Y.L.
and
Shi
F.-G.
, On (L, M)-fuzzy quasi-uniform spaces , Fuzzy Sets Syst 158 (2007 ), 1472 –1485 .
18.
Yue
Y.L.
and
Shi
F.-G.
, L-fuzzy uniform spaces , J Korean Math Soc 44 (6 ) (2007 ), 1383 –1396 .