SUPRA SOFT SEPARATION AXIOMS AND SUPRA IRRESOLUTENESS BASED ON SUPRA B-SOFT SETS

Abstract

This paper introduces supra soft b-separation axioms based on the supra b-
open soft sets which are more general than supra open soft sets. We investigate the relationships between these supra soft separation axioms. Furthermore, with the help of examples it is established that the converse does not hold. We show that, a supra soft topological space (X; t;E) is supra soft b-T1-space, if xE is supra b-closed soft set in for each x 2 X. Also, we prove that xE is supra b-closed soft set for each x  belonds to  X, if (X; t;E) is supra soft T3-space.
For each i = 0; 1; 2; 3; 4, not every supra soft b-open soft subspace of supra soft b-Ti-space is supra soft b-Ti.

Keywords

• Soft sets,Soft topological spaces,Supra soft topological spaces,Supra b-open soft sets,Supra soft b-Ti spaces (i = 1,2; 3; 4),Supra soft continuity,Supra b-irresolute open soft function.

References

1. A. M. Abd El-latif and Serkan Karatas, Supra b-open soft sets and supra b-soft continuity on soft topological spaces, Journal of Mathematics and Computer Applications Research, 5(1)(2015) 1-18.
2. A. M. Abd El-latif, Supra open soft sets and associated soft separation axioms.
3. To appear.
4. M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57(2009)
5. -1553.
6. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986) 87-96.
7. K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64(1994) 159-174.
8. N.Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207(2010) 848-855.

9. N. C agman, Contributions to the Theory of Soft Sets, Journal of New Results in Science, 4(2014) 33-41.
10. S. A. El-Sheikh and A. M. Abd El-latif, Characterization of b-open soft sets in soft topological spaces, Journal of New Theory, 2(2015) 8-18.
11. S. A. El-Sheikh and A. M. Abd El-latif, Decompositions of some types of supra soft sets and soft continuity, International Journal of Mathematics Trends and Technology, 9(1)(2014) 37-56.
12. S. A. El-Sheikh, Rodyna A. Hosny and A. M. Abd El-latif, Characterizations of b-soft separation axioms in soft topological spaces, Information Sciences Letters, 4(3)(2015) 125-133.
13. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Fuzzy soft semi connected properties in fuzzy soft topological spaces, Mathematical Sciences Letters, 4(2)(2015) 171-179.
14. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Gamma-
15. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Gamma-
16. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft connectedness via soft ideals, Journal of New Results in Science, 4(2014) 90-108.
17. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft ideal theory, Soft local function and generated soft topological spaces, Applied Mathematics and Information Sciences, 8(4)(2014) 1595-1603.
18. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft regularity and normality based on semi open soft sets and soft ideals, Applied Mathematics and Information Sciences Letters, 3(2)(2015) 47-55.
19. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft semi compactness via soft ideals, Applied Mathematics and Information Sciences, 8(5)(2014) 2297-2306.
20. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft semi (quasi) Hausdor spaces via soft ideals, South Asian Journal of Mathematics, 4(6)(2014) 265-284.
21. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft semi separation axioms and irresolute soft functions, Annals of Fuzzy Mathematics and Informatics, 8(2)(2014) 305-318.
22. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Some fuzzy soft topological properties based on fuzzy semi open soft sets, South Asian Journal of Mathematics, 4(4)(2014) 154-169.
23. A. Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Supra generalized closed soft sets with respect to an soft ideal in supra soft topological spaces, Applied Mathematics and Information Sciences, 8(4)(2014) 1731-1740.
24. A. Kharal and B. Ahmad and , Mappings on soft classes, New Mathematics and Natural Computation, 7(3)(2011) 471-481.
25. D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, Soft sets theory based optimization, Journal of Computer and Systems Sciences International, 46(6)(2007) 872-880.
26. P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3)(2001) 589-602.
27. P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3)(2001) 677-691.
28. P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45(2003) 555-562.
29. P. Majumdar and S. K. Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications, 59(2010) 1425-1432.
30. A. S. Mashhour, A. A. Allam, F.S. Mahmoud and F. H. Khedr, On supra topological spaces, Indian Journal of Pure and Applied Mathematics, 14(4)(1983) 502-510.
31. D. A. Molodtsov, Soft set theory-rst tresults, Computers and Mathematics with Applications, 37(1999) 19-31.
32. D. Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1(1)(2006) 8-39.
33. Z. Pawlak, Rough sets, Int. J. Comput. Sci., 11(1982) 341-356.
34. D. Pei and D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, in: IEEE, 2(2005) 617-621.
35. Rodyna A. Hosny, Properties of soft b-open sets, Sylwan, 159(4)(2015) 34-49.
36. M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61(2011) 1786-1799.
37. L. A. Zadeh, Fuzzy sets, Information and Control, 8(1965) 338-353.
38. I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2012) 171-185.