On double fuzzy preuniformity
-
1708
Downloads
-
2720
Views
Authors
Vildan Çetkin
- Department of Mathematics, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey.
Halis Aygün
- Department of Mathematics, Kocaeli University, Umuttepe Campus, 41380, Kocaeli, Turkey.
Abstract
In this study, we introduce the notion of double fuzzy uniform space as a view point of the entourage
approach in a strictly two-sided commutative quantale based on powersets of the form \(L^{X\times X}\). We investigate
the relations between double fuzzy preuniformity, double fuzzy topology, double fuzzy interior operator, and
double fuzzy preproximity.
Share and Cite
ISRP Style
Vildan Çetkin, Halis Aygün, On double fuzzy preuniformity, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 4, 263--278
AMA Style
Çetkin Vildan, Aygün Halis, On double fuzzy preuniformity. J. Nonlinear Sci. Appl. (2013); 6(4):263--278
Chicago/Turabian Style
Çetkin, Vildan, Aygün, Halis. "On double fuzzy preuniformity." Journal of Nonlinear Sciences and Applications, 6, no. 4 (2013): 263--278
Keywords
- Double fuzzy topology
- double fuzzy interior operator
- proximity
- uniformity.
MSC
References
-
[1]
M. Alimohammady, E. Ekici, S. Jafari, M. Roohi , Fuzzy minimal separation axioms, J. Nonlinear Sci. Appl., 3 (2010), 157-163.
-
[2]
K. Atanassov , Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
-
[3]
C. L. Chang , Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
-
[4]
V. Çetkin, H. Aygün, On (L;M)-fuzzy interior spaces, Advances in Theoretical and Applied Mathematics, 5 (2010), 177-195.
-
[5]
V. Çetkin, H. Aygün, Lattice valued double fuzzy preproximity spaces, Computers and Mathematics with Applications, 60 (2010), 849-864.
-
[6]
D. Çoker, An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 4 (1996), 749-764.
-
[7]
D. Çoker, M. Demirci, An introduction to intuitionistic fuzzy topological spaces in Šostak's sense , Busefal, 67 (1996), 67-76.
-
[8]
J. Gutierrez Garcia, S. E. Rodabaugh , Order-theoretic, topological, categorical redundancides of interval-valued sets, grey sets, vague sets, interval-valued ''intuitionistic'' sets, ''intuitionistic'' fuzzy sets and topologies, Fuzzy Sets and Systems, 156 (2005), 445-484.
-
[9]
J. Gutierrez Garcia, I. Mardones Perez, M. H. Burton, The relationship between various filter notions on a GL-monoid, J.Math. Anal. Appl., 230 (1999), 291-302.
-
[10]
J. Gutierrez Garcia, M. A. de Prada Vicente, A. P. Šostak, A unified approach to the concept of fuzzy L-uniform spaces, Chapter in [24], (), 81-114.
-
[11]
J. A. Goguen, The fuzzy Tychonoff theorem , J. Math. Anal. Appl., 43 (1973), 734-742.
-
[12]
I. M. Hanafy , \(\beta S^*\)-compactness in L-fuzzy topological spaces, J. Nonlinear Sci. Appl., 2 (2009), 27-37.
-
[13]
U. Höhle, Upper semicontinuous fuzzy sets and applications , J. Math. Anal. Appl., 78 (1980), 659-673.
-
[14]
U. Höhle, E. P. Klement, Non-Classical logic and their applications to fuzzy subsets, Kluwer Academic Publisher, Dordrecht (1995)
-
[15]
U. Höhle , Probabilistic uniformization of fuzzy uniformities, Fuzzy Sets and Systems, 1 (1978), 311-332.
-
[16]
U. Höhle, Many valued topology and its applications , Kluwer Academic Publisher, Boston (2001)
-
[17]
B. Hutton , Uniformities on fuzzy topological spaces , J.Math.Anal.Appl. , 58 (1977), 559-571.
-
[18]
U. M. Abdel-Hamied Hussein , On fuzzy topolgical spaces, Ph.D thesis, Beni-Suef Univ. Egypt (2006)
-
[19]
A. K. Katsaras , Fuzzy quasi-proximities and fuzzy quasi-uniformities, Fuzzy Sets and Syst. , 27 (1988), 335-343.
-
[20]
Y. C. Kim, Y. S. Kim, (\(L,\odot\))-approximation spaces and (\(L,\odot\))-fuzzy quasi-uniform spaces, Information Sciences , 179 (2009), 2028-2048.
-
[21]
W. Kotze , Uniform spaces, Mathematics of fuzzy sets, logic, topology and measure theory , The handbooks of fuzzy sets series vol 3, Kluwer Academic Publishers, Dordrecht (1999)
-
[22]
T. Kubiak, On fuzzy topologies, Ph.D thesis, A. Mickiewicz, Poznan (1985)
-
[23]
Y. M. Liu, M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore (1997)
-
[24]
R. Lowen, Fuzzy uniform spaces, J. Math. Anal. Appl., 82 (1981), 370-385.
-
[25]
A. A. Ramadan, Y. C. Kim, M. K. El-Gayyar, On fuzzy uniform spaces, J. Fuzzy Math., 11 (2003), 279-299.
-
[26]
S. E. Rodabaugh, E. P. Klement, Topological and algebraic structures, in: fuzzy sets, The handbook of recent developments in the mathematics of fuzzy Sets, Trends in logic 20, Kluwer Academic Publishers, Boston (2003)
-
[27]
S. K. Samanta, T. K. Mondal , Intuitionistic gradation of openness: intuitionistic fuzzy topology, Busefal, 73 (1997), 8-17.
-
[28]
S. K. Samanta, T. K. Mondal , On intuitionistic gradation of openness, Fuzzy Sets and Systems, 131 (2002), 323-336.
-
[29]
S. K. Samanta , Fuzzy proximities and fuzzy uniformities, Fuzzy Sets and Systems, 70 (1995), 97-105.
-
[30]
A. P. Šostak, On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palermo ser. II , 11 (1985), 89-102.