Weak Structures on Pythagorean Fuzzy Soft Topological Spaces

Abstract

In this paper, we initiate the topological structures of pythagorean fuzzy soft semi-open sets and pythagorean fuzzy soft semi-closed sets. Furthermore, the concept of pythagorean fuzzy soft semi-interior, pythagorean fuzzy soft semi-closure are presented. Also some related properties are investigated.

Keywords

• Pythagorean fuzzy soft set
• pythagorean fuzzy soft topological spaces
• pythagorean fuzzy soft semi-open(closed) sets
• pythagorean fuzzy soft semi-interior
• pythagorean fuzzy soft semi-closure

Kaynakça

1. Akdag, M. and Ozkan, A. Soft b-open sets and soft b-continuous functions. Mathematical Sciences 8(2), 2014, 124.
2. Akdag, M. and Ozkan, A. On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science 27(4) 2014.
3. Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 1986, 87–96.
4. Athira T.M., John S.J., & Garg H., Entropy and distance measures of Pythagorean fuzzy soft sets and their applications, Journal of Intelligent & Fuzzy Systems 37, 2019, 4071–4084, Doi:10.3233/JIFS-190217
5. Athira T.M., John S.J., & Garg H. A novel entropy measure of Pythagorean fuzzy soft sets. AIMS Mathematics. 5(2), 2020 1050–1061.
6. Chen D., Tsang E.C.C, Yeung D.S., Wang. X., The parameterization reduction of soft sets and its applications. Comput. Math.Appl. 49, 2005, 757-763.
7. Coker D., An introduction of intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems. 88, 1997, 81–89.
8. Feng F., Jun Y.B., Liu X., Li L., An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 234, 2010, 10–20.

9. Guleria A., Bajaj R.K. On pythagorean fuzzy soft matrices operations and their applications in decision making and medical diagnosis. Soft Computing. 23, 2019, 1889–7900, https://doi.org/10.1007/s00500-018-3419-z.
10. Hussain S., A note on soft connectedness. Journal of Egyptian Mathematical Society. 23, 2015, 6–11.
11. Hussain S., Ahmad B., Some properties of soft topological spaces. Computers and Mathematics with Applications. 62, 2011, 4058–4067.
12. Hussain S. On some properties of Intuitionistic fuzzy soft boundary. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 2020, 39–50.
13. Hussain S., On some weak structures in intuitionistic fuzzy soft topological spaces. Italian journal of pure and applied mathematics. 42, 2019, 512–525.
14. Hussain A., Ali M.I. and Mahmood T. Pythagorean fuzzy soft rough sets and their applications in decision-making. Journal of Taibah University for Science. 14(1), 2020, 101–113, doi: 10.1080/16583655.2019.1708541
15. Kirisci M. New type pythagorean fuzzy soft set and decision-making application, arXiv preprint arXiv:1904.04064, 2019. Li Z., Cui R., On the topological structurs of intuitionistic fuzzy soft sets. Annals of fuzzy Mathematics and Informatics. 5, 2013, 229–239.
16. Maji P.K., Biswas R., Roy A.R., Fuzzy soft sets. Journal of Fuzzy Mathematics 9(3), 2001, 589–602.
17. Maji P.K., Biswas R., Roy A.R., Intuitionistic fuzzy soft sets. Journal of fuzzy mathematics 9(3), 2001, 677–692.
18. Maji P.K., Biswas R., Roy A. Soft set theory. Comput. Math. Appl. 45(4-5), 2003, 555–562.
19. Molodtsov D., Soft set theory-first results. Comput. Math. Appl. 37(4-5), 1999, 19–31.
20. Molodtsov D., Leonov V.Y., Kovkov D.V., Soft sets technique and its application. Nechetkie Sistemy i Myagkie Vychisleniya. 9, 2006, 8–39.
21. Olgun M., Unver M. & Yardımcı S. Pythagorean fuzzy topological spaces. Complex Intell. Syst. 5, 2019, 177—183, https://doi.org/10.1007/s40747-019-0095-2.
22. Peng X., Yang Y., Some results for pythagorean fuzzy sets. International Journal of Intelligent Systems. 30(11), 2015, 1133–1160.
23. Peng X., Yang Y., Song J., Jiang Y., Pythagoren fuzzy soft set and its application. Computer Engineering. 41(7), 2015, 224–229.
24. Peng X., New operations for interval-valued pythagorean fuzzy set. Scientia Iranica E. 26(2), 2019, 1049–1076.
25. Roy A.R., Maji P.K., A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 2007, 412418.
26. Riaz M., Naeem K., Aslam M., Afzal D., Ahmahdi F. and Jamal S.S, Multi-criteria Group Decision Making with Pythagorean Fuzzy Soft Topology. Journal of Intelligent and Fuzzy Systems. 2020, 1–18, DOI:10.3233/JIFS-190854.
27. Riaz M., Naeem K., & Afzal, D. Pythagorean m-polar fuzzy soft sets with TOPSIS method for MCGDM. Punjab University Journal of Mathematics. 52(3), 2020, 21–46.
28. Xiao Z., Gong K., Zou Y., A combined forecasting approach based on fuzzy soft sets. J. Comput. Appl. Math. 228, 2009, 326333.
29. Yager R.R. Pythagorean fuzzy subsets. Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada, 57–61,2013.
30. Yager R.R. and Abbasov A.M. Pythagorean membership grades, complex numbers and decision making. Int. J. Intell. Syst. 28(5),2014, 436–452 .
31. Yolcu A., and Ozturk T.Y., Some New Results on Pythagorean Fuzzy Soft Topological Spaces, TWMSJ. App. Eng. Math. Accepted.
32. Zadeh, L.A. Fuzzy Sets. Information and Control. 8, 1965, 338–353.
33. Zou Y., Xiao Z., Data analysis approaches of soft sets under incomplete information. Knowledge-Based Syst. 21, 2008, 941–945.