IJPAM: Volume 113, No. 3 (2017)

Title

$L$-FUZZY $(K,E)$-SOFT PRE-PROXIMITIES
INDUCED BY $L$-FUZZY $(K,E)$-SOFT
QUASI-UNIFORM SPACES

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

In a strictly two-sided commutative quantale having an order reversing involution, we introduce the notion of $L$- fuzzy $(K,E)$-soft pre-proximity spaces and $L$-fuzzy $(K,E)$-soft pre-uniform spaces. We investigate their properties. In particular, an $L$-fuzzy $(K,E)$-soft pre-uniformity induces an $L$-fuzzy $(K,E)$-soft pre-proximity. We give their examples.

History

Received: January 20, 2017
Revised: March 3, 2017
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 03E72, 06A15, 06F07, 54A05.
Key Words and Phrases: Strictly two-sided commutative quantale, $L$-fuzzy $(K,E)$-soft pre-uniform spaces, $(K,E)$-soft pre-proximity spaces.

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Bibliography

1
H. Aktas, N. Cagman, Soft sets and soft groups, Information Sciences, 177 (2007) 2726-2735.

2
M.I. Ali, F. Feng, X.Y. Liu, W.K. Min, M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57 (2009) 1547-2553.

3
A. Aygünoglu, H. Aygün, Introduction to fuzzy soft groups, Computers and Mathematics with Appl., 58(2009) 1279-1286.

4
A. Aygünoglu, V. Cetkin, H. Aygün, An introduction to fuzzy soft topological spaces, Hacettepe Journal of Math. and Stat., 43(2)(2014), 193-204

5
V. Cetkin, Alexander P. Sostak, H. Aygün, An Approach to the Concept of Soft fuzzy Proximity, Abstract and Applied Analysis Stat.,(2014), doi: 10.1155/2014/782583.

6
V. Cetkin, H. Aygün, On fuzzy Soft topogenous structure, Journal of Intelligent and Fuzzy Systems, 27, 1 (2014) 247-255,doi: 10.3233/IFS-130993.

7
F. Feng, Y.B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics, 234 (2010) 10-20.

8
P. Hájek, Metamathematices of Fuzzy Logic,Kluwer Academic Publishers, Dordrecht (1998) doi:10.1007/978-94-011-5300-3.

9
U. Höhle, E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publishers, Boston, (1995)

10
U. Höhle, S.E. Rodabaugh, Mathematics of Fuzzy Sets:Logic, Topology, and Measure Theory, The Handbooks of Fuzzy SetsSeries 3, Kluwer Academic Publishers, Boston, (1999) doi:10.1007/978-1-4615-5079-2.

11
Y.C. Kim and K.C. Min, $L$-fuzzy proximities and $L$-fuzzytopologies, Information Sciences, 173 (2005) 93-113.

12
P.K. Maji, R. Biswas, R. Roy, An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(2002) 1077-1083.

13
P.K. Maji, R. Biswas, R. Roy, Soft set theory, Computers and Mathematics with Applications, 45 (2003) 555-562.

14
D. Molodtsov, Soft set theory first results, Computers and Mathematics with Applications, 37 (1999) 19-31.

15
D. Molodtsov, V.Y. Leonov, D.V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1 (1) (2006) 8-19.

16
Ju-Mok Oh, Y.C.Kim, A.A. Ramadan, $L$- fuzzy $(K,E)$-soft quasi uniform spaces and $L$-fuzzy $(K,E)$-soft topogenous spaces, Int. Journal ofPure and Applied Mathematics , 108(4) (2016) 831-847, : 10.12732/ijpam.v108i4.9. .

17
A.A. Ramadan, Y.C.Kim and M.K.El-Gayyar, On fuzzy preproximity spaces, The Journal of Fuzzy mathematics, 11(2) (2003) 355-378.

18
A.A. Ramadan, E.H. Elkordy, Y.C. Kim , Perfect L-fuzzy topogenous space, L-fuzzy quasi-proximities and L-fuzzy quasi-uniform spaces, Journal ofIntelligent and Fuzzy Systems, 28(6) (2015) 2591-2604.

19
M. Shabir, M. Naz, On soft topological spaces, Computers and Mathematics with Appl., 61 (2011) 1786-1799, doi:10.1016/j.camwa.2011.02.006.

How to Cite?

DOI: 10.12732/ijpam.v113i3.12 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: 501 - 510


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