Soft Topology Generated by L-Soft Sets

Year 2018, Issue: 24, 88 - 100, 14.08.2018

Guzide Senel

Abstract

In this paper, the theory of soft topological space generated by L-soft sets is introduced. As a continuation of the study of operations on L-soft sets, the aim of this paper is to introduce new soft topologies using restricted and extended intersections on L-soft sets and to study the diferences of these soft topologies.

Keywords

Soft sets , L-soft sets , soft topology , L-soft topology

References

• [1] Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Computers and Mathematics with Applications 59, 3458-3463, 2010.
• [2] Ahmad, B., Kharal, A., On fuzzy soft sets, Advances in Fuzzy Systems, 1-6, 2009.
• [3] Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M., On some new operations in soft set theory, Computers and Mathematics with Applications 57, 1547-1553, 2009.
• [4] AygÄunoglu, A. AygÄun, H., Introduction to fuzzy soft groups, Computers and Mathematics with Applications 58, 1279-1286, 2009.
• [5] AygÄunoglu, A. AygÄun, H., Some notes on soft topological spaces, Neural Com- putation and Application, 2011.
• [6] Akta»s, H. ve C» a¸gman, N., Soft sets and soft groups, Information Sciences, 177(1), 2726-2735, 2007.
• [7] Buelohlsavek, R., Fuzzy relational systems, Foundations and Principles, Kluwer, New York 2002.
• [8] Cagman, N., Engino¸glu, S., Soft set theory and uni-int decision making, Euro- pean Journal of Operational Research 207, 848-855, 2010.
• [9] Cagman, N., Engino¸glu, S., Soft matrix theory and its decision making, Com- puters and Mathematics with Applications 59, 3308-3314, 2010.
• 10] Cagman, N., Karata»s, S., Engino¸glu, S., Soft Topology, Computers and Math- ematics with Applications 62 (1), 351-358, 2011.
• [11] Cagman, N., Contributions to the Theory of Soft Sets, Journal of New Result in Science, 4 (2014) 33-41.
• [12] Xueyou Chen and Qingguo Li, Construction of Rough Approximations in Fuzzy Setting, Fuzzy Sets and Systems 158 (2007) 2641-2653.
• [13] Chen, X., Rough Soft Sets in Fuzzy Setting, Lecture Notes in Computer Science 7928 (2013) 530-539.
• [14] Chen, X., Soft sets in fuzzy setting, Annals of Fuzzy Mathematics and Infor- matics, in press.
• [15] Feng F., Jun, Y. B., Liu, X., Li, L., An adjustable approach to fuzzy soft set based decision making, Journal of Computational and Applied Mathematics 234, 10-20, 2010.
• [16] Feng, F., Jun, Y. B., Zhao, X., Soft semirings, Fuzzy Sets and Systems: Theory and Applications 56 (10), 2621-2628, 2008.
• [17] Goguen, J. L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145-174.
• [18] Hussain, S., Ahmad, B., Some properties of soft topological spaces, Computers and Mathematics with Applications (62), 4058-4067, 2011.
• [19] Jiang, Y., Tang, Y., Chen, Q., Wang, J., Tang, s., Extending soft sets with description logics, Computers and Mathematics with Applications 59, 2087- 2096, 2010.
• [20] Jun, Y. B., Lee, K. J., Khan, A., Soft ordered semigroups, Mathematical Logic Quarterly. 56 (1), 42-50, 2010.
• [21] Kalayathankal, S. J., Singh, G. S., A fuzzy soft °ood alarm model, Mathematics and Computers in Simulation 80, 887-893, 2010.
• [22] Maji, P.K., Biswas, R., Roy, A.R., Soft set theory, Computers and Mathematics with Applications 45, 555-562, 2003.
• [23] Majumdar, P., Samanta, S. K., Similarity measure of soft sets, New Mathemat- ics and Natural Computation 4 (1), 1-12, 2008.
• [24] Maji, P. K., Biswas, R., and Roy, A. R., Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589-602.
• [25] Min, W., K., A note on soft topological spaces, Computers and Mathematics with Applications 62, 3524-3528, 2011.
• [26] Molodtsov, D.A., Soft set theory-¯rst results, Computers and Mathematics with Applications 37, 19-31, 1999.
• [27] Park, C.H., Jun, Y.B., Ä OztÄurk, M.A., Soft WS-algebras. Communications of the Korean Mathematical Society. 23 (3), 313-324, 2008.
• [28] Pawlak, Z., Rough sets, International Journal of Computer and Information Science 11 (1982) 341-356.
• [29] Pei, D., Miao D., From soft sets to information systems, Proceedings of Granular Computing 2, 617- 621, 2005.
• [30] Shabir, M., Naz, M., On soft topological spaces, Computers and Mathematics with Applications 61, 1786-1799, 2011.
• [31] Som, T., On the theory of soft sets soft relation and fuzzy soft relation, Proc. of the National Conference On Uncertainty: A Mathematical Approach, 1-9, 2006.
• [32] Sun, Q.M., Zhang, Z.L, Liu, J., Soft sets and soft modules, Proceedings of Rough Sets and Knowledge Technology, Third International Conference China, 403-409, 2008.
• [33] Senel, G., Soft Metric Spaces, Ph.D. Thesis, Gaziosmanpasa University Grad- uate School of Natural and Applied Sciences Department of Mathematics, 92, 2013.
• [34] Senel, G., A New Approach to Hausdor® Space Theory via the Soft Sets, Math- ematical Problems in Engineering 2016 (9), DOI:10.1155/2016/2196743.
• [35] Senel, G., A Comparative Research on the De¯nition of Soft Point, International Journal of Computer Applications 163 (2), DOI:10.5120/ijca2017913471.
• [36] Senel, G., The Parameterization Reduction of Soft Point and its Applications with Soft Matrix, International Journal of Computer Applications 164 (1), DOI:10.5120/ijca2017913564.
• [37] Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965) 338-353.
• [38] Xiao, Z., Gong, K., Xia, S., Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59, 2128-2137, 2010.
• [39] Zorlutuna, I., Akda¸g, M., Min, W. K., Atmaca, S., Remarks on Soft Topological Spaces, Annals of Fuzzy Mathematics and Informatics, 3 (2) (2012), 171-185.
• [40] Zou, Y., Xiao, Z., Data analysis approaches of soft sets under incomplete infor- mation. Knowledge-Based Systems 21, 941-945, 2008.