Some new operations on Pythagorean fuzzy sets

Authors

https://doi.org/10.48313/uda.v1i1.17

Abstract

The concept of Pythagorean Fuzzy Sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to Pythagorean Fuzzy Sets (PFSs).The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In this paper, various operations in Pythagorean Fuzzy Sets are discussed. Some theorems are proved for establishing the properties of Pythagorean fuzzy operators with respect to different Pythagorean fuzzy sets.

Keywords:

Intuitionistic fuzzy sets, Pythagorean fuzzy sets, Operations on pythagorean fuzzy sets

References

  1. [1] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353.
  2. [2] Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20, 87-96.
  3. [3] Abou-Zaid, A. (1989). On fuzzy subnear-ring. Fuzzy sets and systems, 81, 383-393.
  4. [4] Adak, A. K., & Bhowmik, M. (2011). Interval cut-set of interval-valued intuitionistic fuzzy sets. African journal of mathematics
  5. [5] and computer sciences, 4(4), 192-200.
  6. [6] Adak, A. K., Bhowmik, M. & Pal, M. (2012). Interval cut-set of generalized interval-valued intuitionistic fuzzy sets. International
  7. [7] journal of fuzzy system applications, 2(3). 35-50.
  8. [8] Adak, A. K., Salokolaei, D. D. (2021). Some properties rough pythagorean fuzzy sets. Fuzzy information and engineering
  9. [9] (IEEE), 13(4) 420-435.
  10. [10] Adak, A. K., & Kumar, D. (2022). Some properties of Pythagorean fuzzy ideals of Γ- near rings. Palestine journal of mathematics.
  11. [11] (4), 336-346.
  12. [12] Biswas, R. (1990). Fuzzy subgroups and anti-fuzzy subroups. Fuzzy sets and sys. 35(1), 121-124.
  13. [13] Davvaz, B. (2008). Fuzzy R-subgroups with thresholds of near-rings and implication operators. Soft computing, 12, 875-879. [10] Ebrahimnejad, A., Adak, A. K., Jamkhaneh, E.B. (2019). Eigenvalue of intuitionistic fuzzy matrices over distributive lattice.
  14. [14] International journal of fuzzy system applications (IJFSA), 8(1), 1-18.
  15. [15] Yager, R. R., & Abbasov, A. M. (2013). Pythagorean membeship grades, complex numbers and decision making. International
  16. [16] journal of jntelligent systems, 28, 436-452.
  17. [17] Yager, R. R. (2013). Pythagorean fuzzy subsets. In: Proc joint IFSA world congress and NAFIPS annual meeting.
  18. [18] Edmonton, Canada. 57-61.
  19. [19] Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE transaction on fuzzy
  20. [20] systems, 22, 958-965.

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Published

2024-06-02

Issue

Vol. 1 No. 1 (2024): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Adak, A. K. ., Kumar, D. ., & Edalatpanah, S. A. (2024). Some new operations on Pythagorean fuzzy sets. Uncertainty Discourse and Applications, 1(1), 11-19. https://doi.org/10.48313/uda.v1i1.17