A Note on Fuzzy Soft Ditopological Spaces

Year 2019, Volume: 12 Issue: 2, 658 - 667, 31.08.2019

Tuğba Han Dizman

https://doi.org/10.18185/erzifbed.472162

Abstract

In this
study, we define fuzzy soft ditopological spaces as the generalization of soft
ditopological spaces defined by Simsekler et. al.  (2016). 
Fuzzy soft ditopological space is a combination of fuzzy soft
topological and fuzzy soft cotopological spaces which are defined by two
independent structures fuzzy soft open and fuzzy soft closed sets. Also we give
fuzzy soft -continuity
in fuzzy soft topology , fuzzy soft -continuity
in fuzzy soft cotopology and by using these two types of continuity we finally
define the fuzzy soft continuity in a fuzzy soft ditopology.

Bulanık Esnek Ditopolojiler Üzerine Bir Çalışma

Abstract

Bu çalışmada, Simsekler Dizman ve
arkadaşları tarafından (2016) tanımlanan esnek ditopolojik uzayların bir
genelleştirilmesi olan bulanık esnek ditopolojik uzaylar tanımlanmıştır.
Bulanık esnek ditopolojik uzaylar birbirinden bağımsız olarak tanımladığımız
bulanık esnek açık ve bulanık esnek kapalı kümeler kullanılarak tanımlanmış
bulanık esnek topolojiler ve bulanık esnek kotopolojilerin bir kombinasyonudur.
Ayrıca bulanık esnek topolojilerde tanımladığımız τ-süreklilik ve bulanık esnek
kotopolojilerde  -sürekiliği kullanarak bulanık esnek
ditopolojilerde sürekliliği verdik.

Keywords

Fuzzy soft sets, fuzzy soft ditopology

References

• Ahmad, B. and Kharal, A. 2009. On fuzzy soft sets. Adv. Fuzzy Syst., doi:10.1155/2009/586507.
• Ahmad, B. and Hussain, S., 2012. On some structures of soft topology. Mathematical Sciences, DOI: 10.1186/2251-7456-6-64.
• Aktas, H. and Cagman, N. 2007. Soft sets and soft groups. Inform. Sci., 77, 2726-2735.
• Atmaca, S. and Zorlutuna, I. 2013. On fuzzy soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 5(2), 377-386.
• Atmaca, S. and Zorlutuna, I. 2014. On Topological Structures of Fuzzy Parametrized Soft Sets. The Scientific World Journal, Article ID164176.
• Aygunoglu, A. and Aygun, H. 2011. Some notes on soft topological spaces. Neural Computing and Applications, 21(1),113-119.
• Aygunoglu, A., Cetkin, V. and Aygun, H. 2014. An introduction to fs-topological spaces. Hacettepe Journal of Mathematics and Statistics,43(2),197-208.
• Brown, L.M. and Diker, M., 1998. Ditopological texture spaces and intuitionistic sets. Fuzzy Sets and Systems, 98, 217-224.
• Brown, L.M. and Erturk, R. 2000. Fuzzy sets as texture spaces, I. Representation Theorems. Fuzzy Sets and Systems, 110(2), 227-236.
• Brown, L.M. Erturk, R. and Dost, S. 2004. Ditopological texture spaces and fuzzy topology, I. Basic Concepts. Fuzzy Sets and Systems, 147(2), 171-199.
• Brown, L.M., Erturk, R. and Dost, S. 2004. Ditopological texture spaces and fuzzy topology, II. Topological Considerations. Fuzzy Sets and Systems, 147(2), 201-231.
• Cagman, N., Karatas, S., and Enginoglu, S. 2011. Soft topology. Computers and Mathematics with Applications, 62, 351-358.
• Chang, C.L.1968. Fuzzy topological spaces. J. Math. Appl., 24, 182-193.
• Feng, F., Jun, Y.B. and Zhao, X. 2008. Soft semirings. Computers and Mathematics with Applications, 56, 2621-2628.
• Hussain, S. and Ahmad, B. 2011. Some properties of soft topological spaces. Computers and Mathematics with Applications, 62, 4058-4067.
• Kelly, J.L. 1963. Bitopological spaces. Proc. Lond. Math.Soc. III Ser, 13, 71-89.
• Maji, P.K. Biswas, R. and Roy, A.R. 2001. Fuzzy soft sets. J. Fuzzy Math. 9(3), 589-602.
• Min, W.K. 2011. A note on soft topological spaces. Comput. Math. Appl., 62, 3524-3528.
• Molodtsov, D. 1999. Soft set theory-First results. Computers Math. Appl.,37(4/5), 19-31.
• Molodtsov, D. 2004. The theory of soft sets. URSS Publishers, Moscow (in Russian).
• Nazmul, S. and Samanta, S.K. 2010. Soft topological groups. Kochi J. Math., 5,151-161.
• Pazar Varol, B. and Aygun, H. 2012. Fuzzy soft topology. Hacettepe Journal of Mathematics and Statistics, 41(3), 407-419.
• Pazar Varol, B. and Aygun, H. 2013. On soft Hausdorff spaces. Annals of Fuzzy Mathematics and Informatics, 5(1), 15-24.
• Roy, S. and Samanta, T.K. 2012. A note on fuzzy soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3, 305-311.
• Roy, S. and Samanta, T.K. 2013. An introduction to open and closed sets on fuzzy soft topological spaces. Annals of Fuzzy Math. and Inf., 6(2), 425-431.
• Shabir, M. and Naz, M. 2011. On soft topological spaces. Comput. Math. Appl.,61, 1786-1799.
• Simsekler, T. and Yuksel, S. 2013. Fuzzy soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 5(1), 87-96.
• Simsekler Dizman, T., Sostak, A. and Yuksel, S. 2016. Soft Ditopological Spaces. Filomat, 30(1), 209-222.
• Tanay, B. and Kandemir, M.B. 2011. Topological structures of fuzzy soft sets. Computers and Mathematics with Applications, 61, 412-418.
• Zadeh, L.A. 1965. Fuzzy sets. Information and Control, 8, 338-353.
• Zorlutuna, I, Akdag, M., Min, W.K. and Atmaca, S. 2012. Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3(2), 171-185.