Weak Structures on Pythagorean Fuzzy Soft Topological Spaces

Yıl 2020, Cilt: 5 Sayı: 3, 233 - 241, 30.12.2020

Taha Öztürk

Öz

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.

Anahtar Kelimeler

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

• Akdag, M. and Ozkan, A. Soft b-open sets and soft b-continuous functions. Mathematical Sciences 8(2), 2014, 124.
• Akdag, M. and Ozkan, A. On Soft Preopen Sets and Soft Pre Separation Axioms. Gazi University Journal of Science 27(4) 2014.
• Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 1986, 87–96.
• 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
• Athira T.M., John S.J., & Garg H. A novel entropy measure of Pythagorean fuzzy soft sets. AIMS Mathematics. 5(2), 2020 1050–1061.
• 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.
• Coker D., An introduction of intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems. 88, 1997, 81–89.
• 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.
• 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.
• Hussain S., A note on soft connectedness. Journal of Egyptian Mathematical Society. 23, 2015, 6–11.
• Hussain S., Ahmad B., Some properties of soft topological spaces. Computers and Mathematics with Applications. 62, 2011, 4058–4067.
• 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.
• Hussain S., On some weak structures in intuitionistic fuzzy soft topological spaces. Italian journal of pure and applied mathematics. 42, 2019, 512–525.
• 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
• 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.
• Maji P.K., Biswas R., Roy A.R., Fuzzy soft sets. Journal of Fuzzy Mathematics 9(3), 2001, 589–602.
• Maji P.K., Biswas R., Roy A.R., Intuitionistic fuzzy soft sets. Journal of fuzzy mathematics 9(3), 2001, 677–692.
• Maji P.K., Biswas R., Roy A. Soft set theory. Comput. Math. Appl. 45(4-5), 2003, 555–562.
• Molodtsov D., Soft set theory-first results. Comput. Math. Appl. 37(4-5), 1999, 19–31.
• Molodtsov D., Leonov V.Y., Kovkov D.V., Soft sets technique and its application. Nechetkie Sistemy i Myagkie Vychisleniya. 9, 2006, 8–39.
• 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.
• Peng X., Yang Y., Some results for pythagorean fuzzy sets. International Journal of Intelligent Systems. 30(11), 2015, 1133–1160.
• Peng X., Yang Y., Song J., Jiang Y., Pythagoren fuzzy soft set and its application. Computer Engineering. 41(7), 2015, 224–229.
• Peng X., New operations for interval-valued pythagorean fuzzy set. Scientia Iranica E. 26(2), 2019, 1049–1076.
• Roy A.R., Maji P.K., A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 203, 2007, 412418.
• 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.
• 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.
• Xiao Z., Gong K., Zou Y., A combined forecasting approach based on fuzzy soft sets. J. Comput. Appl. Math. 228, 2009, 326333.
• Yager R.R. Pythagorean fuzzy subsets. Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada, 57–61,2013.
• Yager R.R. and Abbasov A.M. Pythagorean membership grades, complex numbers and decision making. Int. J. Intell. Syst. 28(5),2014, 436–452 .
• Yolcu A., and Ozturk T.Y., Some New Results on Pythagorean Fuzzy Soft Topological Spaces, TWMSJ. App. Eng. Math. Accepted.
• Zadeh, L.A. Fuzzy Sets. Information and Control. 8, 1965, 338–353.
• Zou Y., Xiao Z., Data analysis approaches of soft sets under incomplete information. Knowledge-Based Syst. 21, 2008, 941–945.