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On Pythagorean Fuzzy Soft Boundary

Year 2020, Volume: 5 Issue: 3, 242 - 251, 30.12.2020

Abstract

The aim of this paper is to initiate the concept of pythagorean fuzzy soft (PFS) boundary. The characterizations and properties of PFS boundary are discussed and investigated in general as well as in terms of PFS interior and PFS closure.

References

  • Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 1986, 87–96.
  • Akram M., Ilyas F., Garg, H. Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Computing. 24(5), 2020, 3425–3453.
  • Athira T.M., John S.J., & Garg H. A novel entropy measure of Pythagorean fuzzy soft sets. AIMS Mathematics. 5(2), 2020 1050–1061.
  • 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
  • Coker D. An introduction of intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88, 1997, 81–89.
  • Ejegwa P.A. Distance and similarity measures for Pythagorean fuzzy sets. Granular Computing, 5(2), 2020, 225–238.
  • Fei L., & Deng Y. . Multi-criteria decision making in Pythagorean fuzzy environment. Applied Intelligence. 50(2), 2020, 537–561.
  • 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 A., Ali M.I., & Mahmood T. Pythagorean fuzzy soft rough sets and their applications in decision-making. Journal of Taibah University for Science. 14(1), 2020, 101–113.
  • Kirisci M. New type pythagorean fuzzy soft set and decision-making application, arXiv preprint arXiv:1904.04064, 2019.
  • 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.
  • Molodtsov D., Soft set theory-first results. Comput. Math. Appl. 37(4-5), 1999, 19–31.
  • Naeem K., Riaz M., Peng X., & Afzal D. Pythagorean m-polar fuzzy topology with TOPSIS approach in exploring most effectual method for curing from COVID-19. International Journal of Biomathematics, 2050075, 2020.
  • 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.
  • Ozturk T.Y., Soft Mappings on soft generalized topological spaces. Creat. math. inform. 27(2) 2018, 177–190.
  • Ozturk T.Y. On bipolar soft topological spaces. Journal of New Theory 20, 2018, 64-75.
  • Ozturk T.Y. and Bayramov S. Soft mappings space. The Scientific World Journal 2014, 2014.
  • Ozturk, T. Y., & Bayramov, S. Topology on Soft Continuous Function Spaces. Mathematical and Computational Applications, 22(2), 2017, 32.
  • Peng X., Yang Y., Song J., Jiang Y., Pythagoren fuzzy soft set and its application. Computer Engineering. 41(7), 2015, 224–229.
  • 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.
  • Yager R.R. Pythagorean fuzzy subsets. Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada, 2013, 57–61 .
  • 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. TWMS J. App. Eng. Math. Accepted.
  • Zadeh, L.A. Fuzzy Sets. Information and Control. 8, 1965, 338–353.
Year 2020, Volume: 5 Issue: 3, 242 - 251, 30.12.2020

Abstract

References

  • Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 20, 1986, 87–96.
  • Akram M., Ilyas F., Garg, H. Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Computing. 24(5), 2020, 3425–3453.
  • Athira T.M., John S.J., & Garg H. A novel entropy measure of Pythagorean fuzzy soft sets. AIMS Mathematics. 5(2), 2020 1050–1061.
  • 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
  • Coker D. An introduction of intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88, 1997, 81–89.
  • Ejegwa P.A. Distance and similarity measures for Pythagorean fuzzy sets. Granular Computing, 5(2), 2020, 225–238.
  • Fei L., & Deng Y. . Multi-criteria decision making in Pythagorean fuzzy environment. Applied Intelligence. 50(2), 2020, 537–561.
  • 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 A., Ali M.I., & Mahmood T. Pythagorean fuzzy soft rough sets and their applications in decision-making. Journal of Taibah University for Science. 14(1), 2020, 101–113.
  • Kirisci M. New type pythagorean fuzzy soft set and decision-making application, arXiv preprint arXiv:1904.04064, 2019.
  • 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.
  • Molodtsov D., Soft set theory-first results. Comput. Math. Appl. 37(4-5), 1999, 19–31.
  • Naeem K., Riaz M., Peng X., & Afzal D. Pythagorean m-polar fuzzy topology with TOPSIS approach in exploring most effectual method for curing from COVID-19. International Journal of Biomathematics, 2050075, 2020.
  • 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.
  • Ozturk T.Y., Soft Mappings on soft generalized topological spaces. Creat. math. inform. 27(2) 2018, 177–190.
  • Ozturk T.Y. On bipolar soft topological spaces. Journal of New Theory 20, 2018, 64-75.
  • Ozturk T.Y. and Bayramov S. Soft mappings space. The Scientific World Journal 2014, 2014.
  • Ozturk, T. Y., & Bayramov, S. Topology on Soft Continuous Function Spaces. Mathematical and Computational Applications, 22(2), 2017, 32.
  • Peng X., Yang Y., Song J., Jiang Y., Pythagoren fuzzy soft set and its application. Computer Engineering. 41(7), 2015, 224–229.
  • 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.
  • Yager R.R. Pythagorean fuzzy subsets. Proc. Joint IFSA World Congress NAFIPS Annual Meet., 1, Edmonton, Canada, 2013, 57–61 .
  • 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. TWMS J. App. Eng. Math. Accepted.
  • Zadeh, L.A. Fuzzy Sets. Information and Control. 8, 1965, 338–353.
There are 26 citations in total.

Details

Primary Language English
Journal Section Volume V Issue III 2020
Authors

Adem Yolcu 0000-0002-4317-652X

Publication Date December 30, 2020
Published in Issue Year 2020 Volume: 5 Issue: 3

Cite

APA Yolcu, A. (2020). On Pythagorean Fuzzy Soft Boundary. Turkish Journal of Science, 5(3), 242-251.
AMA Yolcu A. On Pythagorean Fuzzy Soft Boundary. TJOS. December 2020;5(3):242-251.
Chicago Yolcu, Adem. “On Pythagorean Fuzzy Soft Boundary”. Turkish Journal of Science 5, no. 3 (December 2020): 242-51.
EndNote Yolcu A (December 1, 2020) On Pythagorean Fuzzy Soft Boundary. Turkish Journal of Science 5 3 242–251.
IEEE A. Yolcu, “On Pythagorean Fuzzy Soft Boundary”, TJOS, vol. 5, no. 3, pp. 242–251, 2020.
ISNAD Yolcu, Adem. “On Pythagorean Fuzzy Soft Boundary”. Turkish Journal of Science 5/3 (December 2020), 242-251.
JAMA Yolcu A. On Pythagorean Fuzzy Soft Boundary. TJOS. 2020;5:242–251.
MLA Yolcu, Adem. “On Pythagorean Fuzzy Soft Boundary”. Turkish Journal of Science, vol. 5, no. 3, 2020, pp. 242-51.
Vancouver Yolcu A. On Pythagorean Fuzzy Soft Boundary. TJOS. 2020;5(3):242-51.