Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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INTUITIONISTIC Q-FUZZY PMS-IDEALS OF A PMS-ALGEBRA

  • Received : 2022.03.07
  • Accepted : 2022.08.25
  • Published : 2022.09.30
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Abstract

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

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References

  1. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. K. T. Atanassov, More on intuitionistic Fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37-45. https://doi.org/10.1016/0165-0114(89)90215-7
  3. S. R. Barbhuiya, Intuitionistic Q-fuzzy Ideals of BG-Algebra, International Journal of Computer Applications, 16 ( 2014), 7-14
  4. B. L. Derseh et al., Intuitionistic fuzzy PMS-ideals of a PMS-algebra, Thai J. Math.,(2022)(Accepted for Publication)
  5. B. L. Derseh et al., Intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, Korean J. Math., 29 (2021), 563-576. https://doi.org/10.11568/KJM.2021.29.3.563
  6. B. L. Derseh et al., Intuitionistic Q-Fuzzy PMS-Subalgebras and Their Level Subsets in a PMSAlgebra, New Mathematics and Natural Computation, (2022) (Accepted for Publication)
  7. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math Japon 23 (1978), 1-26.
  8. K. Iseki, On BCI-algebra,seminar Notes, 8 (1980), 125-130.
  9. K. H. Kim, On intuitionistic Q-fuzzy ideals of semigroups Scientiae Mathematicae Japonicae, 63 (2) (2006), 119-126.
  10. K. H. Kim, On intuitionistic Q-fuzzy semi prime ideals in semi group, Advances in fuzzy Mathematics, 1 (2006), 15-21.
  11. R. Muthuraj, K. H. Manikandan and Sithar Selvevam, Intuitionistic Q-fuzzy Normal HX Group, Journal of Phisical sciences, 15(2011), 95-102.
  12. E. H. Roh, K. H. Kim and J. G. Lee, Intuitionistic Q-Fuzzy Subalgebras of BCK/BCI-algebras, International Mathematical Forum, 1 (2006), 1167-1174
  13. P. M. Sithar Selvam and K. T. Nagalakshmi, Fuzzy PMS ideals in PMS-algebras, Annals of pure and applied mathematics, 12 (2016), 153-159. https://doi.org/10.22457/apam.v12n2a6
  14. P. M. Sithar Selvam and K. T. Nagalakshmi, On PMS-algebras, Transylvanian Review, 24 (2016), 1622-1628.
  15. A. Solairaju and R. Nagarajan , A new structure and construction of Q-fuzzy groups, Advances in fuzzy mathematics, 4 (2009), 23-29.
  16. J. D. Yadav,Y. S. Pawar, Intuitionistic Q-fuzzy ideals of near-rings, Vietnam Journal Mathematics, 40 (1) (2012), 195-105.
  17. S. Yamak and S. Yilmaz, On intuitionistic Q-fuzzy R-subgroups of near-rings, Int. Math. Forum. 2 (59) (2007), 2899-2910. https://doi.org/10.12988/imf.2007.07264
  18. L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X