IJPAM: Volume 108, No. 2 (2016)


Jung Mi Ko$^1$, Ju-Mok Oh$^2$
$^{1,2}$Department of Mathematics
Gangneung-Wonju University
Gangneung, Gangwondo, 210-702, KOREA

Abstract. In this paper, we introduce the notion of $L$-fuzzy $(K,E)$-soft preclosure spaces. We investigate two $L$-fuzzy $(K,E)$-soft preclosure spaces induced by an $L$-fuzzy $(K,E)$-soft quasi-uniform space. Also, we study the relationship among $L$-fuzzy $(K,E)$-soft preclosure spaces, $L$-fuzzy $(K,E)$-soft topological spaces and $L$-fuzzy $(K,E)$-soft quasi-uniform space. Finally, we give their examples.

Received: April 29, 2016

Revised: April 29, 2016

Published: October 1, 2016

AMS Subject Classification: 03E72, 06A15, 06F07, 54A05

Key Words and Phrases: complete residuated lattice, $L$-fuzzy $(K,E)$-soft preclosure space, $L$-fuzzy $(K,E)$-soft quasi-uniform space, $L$-fuzzy $(K,E)$-soft topological space
Download paper from here.


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

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

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.

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.

V. Cetkin, H. Aygün, On soft fuzzy closure and interior operator, Utilitas Mathematics, In press.

D. Čimoka, A.Šostak, $L$-fuzzy syntopogenous structures, Part I: Fundamentals and application to $L$-fuzzy topologies, $L$-fuzzy proximities and $L$-fuzzy uniformities, Fuzzy Sets and Systems, 232 (2013), 74-97.

F. Feng, X. Liu, V.L. Fotea, Y.B. Jun, Soft sets and soft rough sets, Information Sciences, 181 (2011), 1125-1137,doi: 10.1016/j.ins.2010.11.004.

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

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: 10.1007/978-1-4615-5079-2.

Y.C. Kim, A.A. Ramadan, $L$-fuzzy $(K,E)$-soft topologies and $L$-fuzzy $(K,E)$-soft closure operators, Int. Journal of Pure and Applied Math. 107 (4) (2016), 1073-1088,doi: 10.12732/ijpan.v 107i4.24.

P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3)(2001), 589-602.

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

P. Majumdar, S.K. Samanta, Generalized fuzzy soft sets, Computers Mathematics with Appl., 59(2010), 1425-1432.

D. Molodtsov, Soft set theory, Computers Mathematics with Appl., 37(1999), 19-31.

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

D. Pei, D. Miao, From soft sets to information systems, Granular Computing,2005 IEEE,International Conferences on (2)(2005),617-621.

A.A. Ramadan, Y.C. Kim, $L$-fuzzy $(K,E)$-soft pre-uniformity and $L$-fuzzy $(K,E)$-soft pre-proximity, The Korean Journal of Mathematics (submitted)(2016)

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.

A.R. Roy, P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, International of Computational and Applied Mathematics, 203(2007),412-418.

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.

B. Tanay,M.B. Kandemir, Topological structures of fuzzy soft sets, Computers and Mathematics with Appl., 61(2011),412-418, , doi: 10.1016/j.camwa.2011.03.056.


DOI: 10.12732/ijpam.v108i2.6 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 108
Issue: 2
Pages: 275 - 290

$L$-FUZZY $(K,E)$-SOFT QUASI-UNIFORMITIES AND $L$-FUZZY $(K,E)$-SOFT PRECLOSURE OPERATORS%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

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