Research Article
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Bipolar Pythagorean Fuzzy Subring of a Ring

Year 2020, Issue: 30, 8 - 20, 26.03.2020

Rajan Jansı Krishnaswamy Mohana

Abstract

In this paper, we study some of the properties of bipolar Pythagorean fuzzy subring of a ring and prove some results on these. We derive some important theorems and intersection and product are applied into the bipolar Pythagorean fuzzy subring of a ring.

Keywords

Bipolar Pythagorean fuzzy set bipolar Pythagorean fuzzy subring bipolar pythagorean fuzzy product

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87- 90.
  • R. R. Yager, Pythagorean Fuzzy Subsets, In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013) 57-61.
  • R. R. Yager, A. M. Abbasov, Pythagorean Membership Grades, Complex Numbers and Decision Making, International Journal of Intelligent Systems 28 (2013) 436-452.
  • R. R. Yager, Pythagorean Membership Grades in Multicriteria Decision Making, IEEE Transactions on Fuzzy Systems 22 (2014) 958-965.
  • Y. B. Jun, S. Z. Song, Subalgebras and Closed Ideals of BCH-Algebra Based on Bipolar Valued Fuzzy Sets, Scientiae Mathematicae Japonicae Online 2 (2008) 427-437.
  • P. Bosc, O. Pivert, On a Fuzzy Bipolar Relational Algebra, Information Sciences 219 (2013) 1-16.
  • K. J. Lee, Bipolar Fuzzy Subalgebras and Bipolar Fuzzy Ideals of BCK/BCI-Algebras, Bulletin of the Malaysian Mathematical Sciences Society 32(3) (2009) 361-373.
  • K. M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, Proc. International Conference on Intelligent Technologies, Thailand, (2000) 307-312.
  • J. Chen, S. Li, S. Ma, X. Wang, m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets, The Scientific World Journal (2014) http://dx.doi.org/10.1155/2014/416530.
  • W. Liu, Fuzzy Invariant Subgroups and Fuzzy Ideals, Fuzzy Sets and Systems 8 (1982) 133-139.
  • K. Hur, H. W. Kang, H. K. Song, Intuitionistic Fuzzy Subgroups and Subrings, Honam Mathematical Journal 25 (2003) 19-41.
  • M. F. Marashdeh, A. R. Salleh, Intuitionistic Fuzzy Rings, International Journal of Algebra 5 (2011) 37-47.
  • K. Mohana, R. Jansi, Bipolar Pythagorean Fuzzy Sets and Their Application Based on Multi-Criteria Decision-Making Problems, International Journal of Research Advent in Technology 6 (2018) 3754-764.
  • K. Meena, K. V. Thomas, Intuitionistic L-Fuzzy Subrings, International Mathematical Forum 6 (2011) 2561-2572.

Year 2020, Issue: 30, 8 - 20, 26.03.2020

Rajan Jansı Krishnaswamy Mohana

Abstract

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87- 90.
  • R. R. Yager, Pythagorean Fuzzy Subsets, In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013) 57-61.
  • R. R. Yager, A. M. Abbasov, Pythagorean Membership Grades, Complex Numbers and Decision Making, International Journal of Intelligent Systems 28 (2013) 436-452.
  • R. R. Yager, Pythagorean Membership Grades in Multicriteria Decision Making, IEEE Transactions on Fuzzy Systems 22 (2014) 958-965.
  • Y. B. Jun, S. Z. Song, Subalgebras and Closed Ideals of BCH-Algebra Based on Bipolar Valued Fuzzy Sets, Scientiae Mathematicae Japonicae Online 2 (2008) 427-437.
  • P. Bosc, O. Pivert, On a Fuzzy Bipolar Relational Algebra, Information Sciences 219 (2013) 1-16.
  • K. J. Lee, Bipolar Fuzzy Subalgebras and Bipolar Fuzzy Ideals of BCK/BCI-Algebras, Bulletin of the Malaysian Mathematical Sciences Society 32(3) (2009) 361-373.
  • K. M. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, Proc. International Conference on Intelligent Technologies, Thailand, (2000) 307-312.
  • J. Chen, S. Li, S. Ma, X. Wang, m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets, The Scientific World Journal (2014) http://dx.doi.org/10.1155/2014/416530.
  • W. Liu, Fuzzy Invariant Subgroups and Fuzzy Ideals, Fuzzy Sets and Systems 8 (1982) 133-139.
  • K. Hur, H. W. Kang, H. K. Song, Intuitionistic Fuzzy Subgroups and Subrings, Honam Mathematical Journal 25 (2003) 19-41.
  • M. F. Marashdeh, A. R. Salleh, Intuitionistic Fuzzy Rings, International Journal of Algebra 5 (2011) 37-47.
  • K. Mohana, R. Jansi, Bipolar Pythagorean Fuzzy Sets and Their Application Based on Multi-Criteria Decision-Making Problems, International Journal of Research Advent in Technology 6 (2018) 3754-764.
  • K. Meena, K. V. Thomas, Intuitionistic L-Fuzzy Subrings, International Mathematical Forum 6 (2011) 2561-2572.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Rajan Jansı This is me

Krishnaswamy Mohana This is me

Publication Date March 26, 2020
Submission Date June 27, 2019
Published in Issue Year 2020 Issue: 30

Cite

APA Jansı, R., & Mohana, K. (2020). Bipolar Pythagorean Fuzzy Subring of a Ring. Journal of New Theory(30), 8-20.
AMA Jansı R, Mohana K. Bipolar Pythagorean Fuzzy Subring of a Ring. JNT. March 2020;(30):8-20.
Chicago Jansı, Rajan, and Krishnaswamy Mohana. “Bipolar Pythagorean Fuzzy Subring of a Ring”. Journal of New Theory, no. 30 (March 2020): 8-20.
EndNote Jansı R, Mohana K (March 1, 2020) Bipolar Pythagorean Fuzzy Subring of a Ring. Journal of New Theory 30 8–20.
IEEE R. Jansı and K. Mohana, “Bipolar Pythagorean Fuzzy Subring of a Ring”, JNT, no. 30, pp. 8–20, March 2020.
ISNAD Jansı, Rajan - Mohana, Krishnaswamy. “Bipolar Pythagorean Fuzzy Subring of a Ring”. Journal of New Theory 30 (March 2020), 8-20.
JAMA Jansı R, Mohana K. Bipolar Pythagorean Fuzzy Subring of a Ring. JNT. 2020;:8–20.
MLA Jansı, Rajan and Krishnaswamy Mohana. “Bipolar Pythagorean Fuzzy Subring of a Ring”. Journal of New Theory, no. 30, 2020, pp. 8-20.
Vancouver Jansı R, Mohana K. Bipolar Pythagorean Fuzzy Subring of a Ring. JNT. 2020(30):8-20.
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