On Soft Topology

Yıl 2015, Cilt: 2 Sayı: 3, 23 - 38, 17.06.2015

Serdar Enginoğlu Naim Çağman Serkan Karataş Tuğçe Aydın

https://doi.org/10.31202/ecjse.67135

Cited By: 12

Öz

Soft set theory was introduced by Molodtsov in 1999. Until now many versions of it have been developed and applied to a lot of areas from algebra to decision making problems. One of these areas is Soft Topology [Çağman, N., Karataş, S., Enginoglu, S., Soft topology, Computers and Mathematics with Applications, 62, 351-358, 2011]. However, it has some difficulties and mistakes. In this paper, for further study on the soft topology, we have made fit this concept which is important for development of the concept of soft sets by decontaminating from its own inconsistencies. We finally discuss this concept later on works

Anahtar Kelimeler

Soft sets, soft topology, soft open sets, soft single point set, soft limit point, soft Hausdorff space

On Soft Topology

Öz

Soft set theory was introduced by Molodtsov in 1999. Until now its many versions have been developed and applied to a lot of areas from algebra to decision making problems. One of these area is Soft Topology [Çağman, N., Karataş, S., Enginoglu, S., Soft topology, Computers and Mathematics with Applications, 62, 351-358, 2011.] However, it has some difficulties and mistakes.

In this paper, for further study on the soft topology, we have made fit this concept which is important for development of the concept of soft sets by decontaminating from its own inconsistencies. We finally discuss this concept later on works.

Anahtar Kelimeler

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Kaynakça

• Acar U., Koyuncu F., Tanay B., 2010. Soft sets and soft rings. Computers and Mathematics with Applications, 59: 3458-3463.
• Aktaş H., Çağman N., 2007. Soft sets and soft groups. Information Sciences, 177: 2726-2735.
• Ali M.I., Feng F., Liu X., Min W.K., Shabir M., 2009. On some new operations in soft set theory. Computers and Mathematics with Applications, 57: 1547-1553.
• Aygünoğlu A., Aygün H., 2011. Some notes on soft topological spaces. Neural Computing and Applications, DOI 10.1007/s00521-011-0722-3.
• Çağman N., Enginoğlu S., 2010a. Soft set theory and uni-int decision making. European Journal of Operational Research, 207: 848-855.
• Çağman N., Enginoglu S., 2010b. Soft matrix theory and its decision making. Computers and Mathematics with Applications, 59: 3308-3314.
• Çağman N., Karataş S., Enginoglu S., 2011. Soft topology. Computers and Mathematics with Applications, 62: 351-358.
• Feng F., Jun Y.B., Zhao X., 2008. Soft semirings. Computers and Mathematics with Applications, 56: 2621-2628.
• Georgiou D.N., Megaritis A.C., Petropoulos V.I., 2013. On soft topological spaces. Applied Mathematics and Information Sciences, 7 (5): 1889-1901.
• Georgiou D.N., Megaritis A.C., 2014. Soft set theory and topology. Applied General Topology, 15 (1): 93-109.
• Hazra H., Majumdar P., Samanta S.K., 2012. Soft Topology. Fuzzy Information and Engineering, 1: 105-115.
• Hussain S., Ahmad B., 2011. Some properties of soft topological spaces. Computers and Mathematics with Applications, 62: 4058-4067.
• Jiang Y., Tang Y., Chen Q., Wang J., Tang S., 2010. Extending soft sets with description logics. Computers and Mathematics with Applications, 59: 2087-2096.
• Jun Y.B., Park C.H., 2009. Applications of soft sets in Hilbert algebras. Iranian Journal Fuzzy Systems, 6 (2): 75-86.
• Jun Y.B., Lee K.J., Khan, A., 2010. Soft ordered semigroups. Mathematical Logic Quarterly, 56 (1): 42-50.
• Kovkov D.V., Kolbanov V.M., Molodtsov D.A., 2007. Soft sets theory-based optimization. Journal of Computer and Systems Sciences International, 46 (6): 872-880.
• Li Z., Xie T., 2014. The relationship among soft sets, soft rough sets and topologies. Soft Comput, 18: 717-728.
• Maji P.K., Biswas R., Roy A.R., 2003. Soft set theory. Computers and Mathematics with Applications, 45: 555-562.
• Maji P.K., Roy A.R., Biswas R., 2002. An application of soft sets in a decision making problem. Computers and Mathematics with Applications, 44: 1077-1083.
• Majumdar P., Samanta S.K., 2008. Similarity measure of soft sets. New Mathematics and Natural Computation, 4 (1): 1-12.
• Min W.K., 2011. A note on soft topological spaces. Computers and Mathematics with Applications, 62: 3524-3528.
• Min W.K., 2014. Soft sets over a common topological universe. Journal of Intelligent and Fuzzy Systems, 26: 2099-2016.
• Molodtsov D., 1999. Soft set theory-first results. Computers and Mathematics with Applications, 37: 19-31.
• Molodtsov D., Leonov V.Y., Kovkov D.V., 2006. Soft sets technique and its application. Nechetkie Sistemy i Myagkie Vychisleniya, 1(1):8-39.
• Nazmul S.K., Samanta S.K., 2014. Some properties of soft topologies and group soft topologies. Annals of Fuzzy Mathematics and Informatics, 8 (4): 645-661.
• Pei D., Miao D., 2005. From soft sets to information systems, In: Proceedings of Granular Computing (Eds: X. Hu, Q. Liu, A. Skowron, T.Y. Lin, R.R. Yager, B.Zhang), (Vol. 2, pp. 617-621). IEEE.
• Peyghan E., Samadi B., Tayebi A., 2013. About soft topological spaces. Journal of New Results in Science, 2: 60-75.
• Qin K., Hong Z., 2010. On soft equality. Journal of Computational and Applied Mathematics, 234: 1347-1355.
• Roy S., Samanta T.K., 2014. A note on a soft topological space. Journal of Mathematics, 46 (1): 19-24.
• Sezgin A., Atagün A.O., 2011. On operations of softsets. Computers and Mathematics with Applications, 61: 1457-1467.
• Shabir M., Naz M., 2011. On soft topological spaces. Computers and Mathematics with Applications, 61: 1786-1799.
• Varol B.P., Shostak A., Aygün H., 2012. A new approach to soft topology. Hacettepe Journal of Mathematics and Statistics, 41 (5): 731-741.
• Zorltuna İ., Akdağ M., Min W.K., Atmaca S., 2012. Remarks on soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 3 (2): 171-185.