Research Article
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Soft Topology Generated by L-Soft Sets

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

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.

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

Abstract

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.
There are 40 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Guzide Senel

Publication Date August 14, 2018
Submission Date March 22, 2018
Published in Issue Year 2018 Issue: 24

Cite

APA Senel, G. (2018). Soft Topology Generated by L-Soft Sets. Journal of New Theory(24), 88-100.
AMA Senel G. Soft Topology Generated by L-Soft Sets. JNT. August 2018;(24):88-100.
Chicago Senel, Guzide. “Soft Topology Generated by L-Soft Sets”. Journal of New Theory, no. 24 (August 2018): 88-100.
EndNote Senel G (August 1, 2018) Soft Topology Generated by L-Soft Sets. Journal of New Theory 24 88–100.
IEEE G. Senel, “Soft Topology Generated by L-Soft Sets”, JNT, no. 24, pp. 88–100, August 2018.
ISNAD Senel, Guzide. “Soft Topology Generated by L-Soft Sets”. Journal of New Theory 24 (August 2018), 88-100.
JAMA Senel G. Soft Topology Generated by L-Soft Sets. JNT. 2018;:88–100.
MLA Senel, Guzide. “Soft Topology Generated by L-Soft Sets”. Journal of New Theory, no. 24, 2018, pp. 88-100.
Vancouver Senel G. Soft Topology Generated by L-Soft Sets. JNT. 2018(24):88-100.


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