INTUITIONISTIC FUZZY TRANSLATION AND MULTIPLICATION OF PMS-SUBALGEBRAS OF A PMS-ALGEBRA

Document Type : Original Manuscript

Author

Department of Mathematics, Debre Markos University, P.O. Box 79, Debre Markos, Ethiopia.

10.22044/jas.2024.14102.1801

Abstract

In this paper, we apply the concepts of intuitionistic fuzzy translations and intuitionistic fuzzy multiplications of intuitionistic fuzzy sets to the PMS-subalgebras of a PMS algebra and investigate several related results. The relationships between intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and intuitionistic fuzzy ω-translations, and intuitionistic fuzzy ζ-multiplications of intuitionistic fuzzy PMS-subalgebras are discussed. Finally, we discuss the ideas of intuitionistic fuzzy magnified ζω - translations of intuitionistic fuzzy PMS-subalgebras of a PMS-algebra and investigate some associated results.

Keywords

References

1. A. Almuhaimeed, Applications on fuzzy translation and fuzzy multiplication of KUalgebras, Int. J. Math. Comput. Sci., 17(2) (2022), 667–677.
 
2. H. A. Alshehri, Fuzzy translation and fuzzy multiplication in BRK-algebras, Eur. J. Pure Appl. Math., 14(3) (2021), 737–745.
 
3. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87–96.
 
4. K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(2) (1994), 137–142.
 
5. B. L. Derseh, B. A. Alaba and Y. G. Wondifraw, Intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, Korean J. Math., 29(3) (2021), 563–576.
 
6. A. T. Hameed, M. S. Mahdi Zabiba and N. H. Malik, Magnified translation of intuitionistic fuzzy AT-ideals on AT-algebra, J. Discrete Math. Sci. Cryptogr., 24(6) (2021),1645–1650.
 
7. K. Iseki, On BCI-algebras, Mathematics Seminar Notes, 8 (1980), 125–130.
 
8. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Mathematica Japonica, 23 (1978), 1–26.
 
9. M. Kaviyarasu and K. Indhira, Fuzzy Translation of INK-ideal of INK-algebras, International Journal of Innovative Technology and Exploring Engineering, 8(12) (2019), 4319–4322.
 
10. M. Kaviyarasu, K. Indhira and V. M. Chandrasekaran, Intuitionistic fuzzy translation on INK-Algebra, Advances in Mathematics: Scientific Journal, 9(1) (2020), 295–303. 
 
11. M. Khalid, Z. Iqbal and R. Iqbal, Intuitionistic Fuzzy Magnified Translation of PSAlgebra, Journal of New Theory, 35 (2021), 32–47.
 
12. M. Khalid, R. Iqbal, S. Zafar and H. Khalid, Intuitionistic fuzzy translation and multiplication of G-algebra, The Journal of Fuzzy Mathematics, 27(3) (2019), 543–559.
 
13. D. Ramesh, K. K. Rao, R. D. Prasad, N. Srimannarayana and B. Satyanarayana, Translations of intuitionistic fuzzy subalgebras in BF-algebras, Advances in Mathematics: Scientific Journal, 9(10) (2020), 8837–8844.
 
14. T. Senapati, Translation of Intuitionistic Fuzzy B-Algebras, Fuzzy Information and Engineering, 7(4) (2015), 389–404.
 
15. T. Senapati, M. Bhowmik and M. Pal, Atanassov’s Intuitionistic Fuzzy Translations of Intuitionistic Fuzzy H-Ideals in BCK/BCI-Algebras, Notes on Intuitionistic Fuzzy Sets, 19(1) (2013), 32–47.
 
16. T. Senapati, M. Bhowmik, M. Pal and B. Davvaz, Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras and ideals in BCK\BCI-algebras, Eurasian Math. J., 6(1) (2015), 96–114.
 
17. T. Senapati, A. Iampan and R. Chinram, Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras in BG-algebras, TWMS Journal of Applied and Engineering Mathematics, 13(3) (2023), 911–919.
 
18. P. M. Sithar Selvam and K. T. Nagalakshmi, Fuzzy PMS ideals in PMS-algebras, Annals of pure and applied mathematics, 12 (2016), 153–159.
 
19. P. M. Sithar Selvam and K. T. Nagalakshmi, On PMS-algebras, Transylvanian Review, 24 (2016), 1622–1628.
 
20. Y. G. Wondifraw, B. A. Alaba and B. L. Derseh, Intuitionistic fuzzy PMS-ideals of a PMS-algebra, Thai J. Math., 20(4) (2022), 1535–1548.
 
21. L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353 
Journal of Algebraic Systems
Volume 14, Issue 2
April 2026
Pages 245-262

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