IJPAM: Volume 113, No. 3 (2017)

Title

SOME PROPERTIES OF $L$-FUZZY PREUNIFORMITIES,
$L$-FUZZY NEIGHBORHOOD SYSTEMS
AND $L$-FUZZY TOPOLOGIES

Authors

Ju-Mok Oh$^{1}$, A.A.Ramadan$^{2}$, Yong Chan Kim$^{3}$
$^{1,3}$ Department of Mathematics
Gangneung-Wonju University
Gangneung, Gangwondo 25457, KOREA
$^{2}$Mathematics Department
Faculty of Science
Beni-Suef University
Beni-Suef, Egypt

Abstract

IThis article gives results on $L$-fuzzy preuniformities, $L$-fuzzy neighborhood systems and $L$-fuzzy topologies in complete residuated lattices, and includes some properties. The notion of their continuity property is investigated

History

Received: January 20, 2017
Revised: March 3, 2017
Published: March 28, 2017
Corrections: April 3, 2017: There are some editorial typos in original publication: see received, revised, first letter in abstract. The original publication is available here. 

AMS Classification, Key Words

AMS Subject Classification: 03E72, 06A15, 06F07, 54A05.
Key Words and Phrases: Complete residuated lattice, $L$-fuzzy neighborhood space, $L$-fuzzy preuniform space, $L$-fuzzy topologies.

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
R. Badard, A.A. Ramadan, A.S. Mashhour, Smooth preuniform and proximity spaces, Fuzzy Sets and Systems, 59 (1993), 95-107.

2
R. Bělohlávek,Fuzzy Relational Systems, Kluwer Academic Publishers, New York (2002), doi: https://doi.org/10.1007/978-1-4615-0633-1.

3
Fang Jinming, $I$-fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems, 158 (2007), 2359-2374.

4
J. Fang, The relationship between L-ordered convergence structures and strong L-topologies, Fuzzy Sets and Systems, 161 (2010), 2923-2944.

5
J.Gutiérrez García, I. Mardones Peerez, M.H. Burton, The relationship between various filter notions on a GL-monoid, J. Math. Anal. Appl., 230 (1999), 291- 302.

6
J.Gutiérrez García, M. A. de Prade Vicente, A.P. Šostak, A unified approach to the concept of fuzzy Luniform spaces, Chapter 3, 81-114 in [23].

7
P. Hájek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998, doi: https://doi.org/10.1007/978-94-011-5300-3.

8
U. Höhle, S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston (1999), doi: https://doi.org/10.1007/978-1-4615-5079-2.

9
B. Hutton, Uniformities in fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 74-79, doi: https://doi.org/10.1016/0022-247x(77)90192-5.

10
A.K. Katsaras, On fuzzy uniform spaces, J. Math. Anal. Appl., 101 (1984), 97-113, doi: https://doi.org/10.1016/0022-247x(84)90060-x.

11
Y.C. Kim, A.A. Ramadan, M. A. Usama, $L$-fuzzy Uniform Spaces, The Journal of Fuzzy Mathematics, 14 (2006), 821-850.

12
J.M. Ko, J.M. Oh, Relationships between $L$-neighborhood systems and $L$-fuzzy topologies, Int.J. Pure and Applied Math., 112(3), (2017) 631-643, doi: https://doi.org/10.12732/ijpam.v112i3.14.

13
W. Kotzé, Uniform spaces, Chapter 8, 553-580 in [8].

14
T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz Uniformity, Poznan, Poland, (1985)

15
R. Lowen, Fuzzy uniform spaces, J. Math. Anal. Appl., 82 (1981), 370-385.

16
R. Lowen, Fuzzy neighborhood spaces, Fuzzy Sets and Systems, 7 (1982), 165-189.

17
H. Lai, D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157 (2006), 1865-1885.

18
A.A. Ramadan,Y.C. Kim, M.K. El-Gayyar, On fuzzy uniform spaces, The Journal of Fuzzy Mathematics, 11 (2003), 279-299.

19
A.A. Ramadan, E.H.Elkordy, Yong Chan Kim, Relationships between $L$-fuzzy quasi-uniform stuctures and $L$-fuzzy topologies, Journal of Intelligent and Fuzzy Systems, 28 (2015), 2319-2327.

20
A.A. Ramadan, On $L$-fuzzy interior operators and $L$-fuzzy quasi-uniform spaces, Journal of Intelligent and Fuzzy Systems, in press.

21
S.E. Rodabaugh, A theory of fuzzy uniformities withapplications to the fuzzy real lines, J. Math. Anal. Appl., 129 (1988), 37-70.

22
S.E. Rodabaugh, E.P. Klement, Topological and Algebraic Structures In Fuzzy Sets, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Kluwer Academic Publishers, Boston, Dordrecht, London, (2003)

23
A.P. Šostak, On a fuzzy topological structure, Suppl.,Rend Circ. Matem. Palermo, Ser. II [11] (1985), 125- 186.

24
A.P. Šostak,Towards the theory of M-approximatesystems, Fuzzy Sets and Systems, 161 (2010), 2440- 2461.

25
E. Turunen,Mathematics Behind Fuzzy Logic, ASpringer-Verlag Co., Heidelberg (1999).

How to Cite?

DOI: 10.12732/ijpam.v113i3.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 3
Pages: 511 - 522

 

; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).