# Intuitionistic Q-fuzzy PMS-ideals of a PMS-Algebra

## Main Article Content

## 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.

## Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

## References

[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87–96. Google Scholar

[2] K. T. Atanassov, More on intuitionistic Fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37–45. Google Scholar

[3] S. R. Barbhuiya, Intuitionistic Q-fuzzy Ideals of BG-Algebra, International Journal of Computer Applications, 16 ( 2014), 7–14. Google Scholar

[4] B. L. Derseh et al., Intuitionistic fuzzy PMS-ideals of a PMS-algebra, Thai J. Math.,(2022)(Accepted for Publication) Google Scholar

[5] B. L. Derseh et al., Intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, Korean J. Math., 29 (2021), 563–576. Google Scholar

[6] B. L. Derseh et al., Intuitionistic Q-Fuzzy PMS-Subalgebras and Their Level Subsets in a PMS- Algebra, New Mathematics and Natural Computation, (2022) (Accepted for Publication) Google Scholar

[7] K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math Japon 23 (1978), 1–26. Google Scholar

[8] K. Iseki, On BCI-algebra,seminar Notes, 8 (1980), 125–130. Google Scholar

[9] K. H. Kim, On intuitionistic Q-fuzzy ideals of semigroups Scientiae Mathematicae Japonicae, 63 (2) (2006), 119–126. Google Scholar

[10] K. H. Kim, On intuitionistic Q-fuzzy semi prime ideals in semi group, Advances in fuzzy Mathematics, 1 (2006), 15–21. Google Scholar

[11] R. Muthuraj, K. H. Manikandan and Sithar Selvevam, Intuitionistic Q-fuzzy Normal HX Group, Journal of Phisical sciences, 15(2011), 95–102. Google Scholar

[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 Google Scholar

[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. Google Scholar

[14] P. M. Sithar Selvam and K. T. Nagalakshmi, On PMS-algebras, Transylvanian Review, 24 (2016), 1622–1628. Google Scholar

[15] A. Solairaju and R. Nagarajan , A new structure and construction of Q-fuzzy groups, Advances in fuzzy mathematics, 4 (2009), 23–29. Google Scholar

[16] J. D. Yadav,Y. S. Pawar, Intuitionistic Q-fuzzy ideals of near-rings, Vietnam Journal Mathe- matics, 40 (1) (2012), 195–105. Google Scholar

[17] S. Yamak and S. Yilmaz, On intuitionistic Q-fuzzy R-subgroups of near-rings, Int. Math. Forum. 2 (59) (2007), 2899–2910. Google Scholar

[18] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. Google Scholar