(T, S)-norms over intuitionistic fuzzy implicative and positive implicative ideals in BCK-algebra

Authors

https://doi.org/10.48313/uda.vi.76

Abstract

In this paper, we use the notion of T-norm  and S-norm  to introduce intuitionistic fuzzy implicative ideals, intuitionistic fuzzy positive implicative ideals, in BCK-algebras. Next we study the links between them and investigate properties related properties under -norms.

Keywords:

Intuitionistic fuzzy implicative ideals, Intuitionistic fuzzy positive implicative ideals, T-norm and S-norm

References

  1. [1] Imai, Y., & Iséki, K. (1966). On axiom systems of propositional calculi. XIV. Proceedings of the japan academy, 42(1), 19–22. https://doi.org/10.3792/pja/1195522169
  2. [2] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
  3. [3] Alcheikh, M., & Sabouh, A. (2019). A study of fuzzy ideals in BCK algebra. Journal of mathematics research, 11(5), 11–15. https://doi.org/10.5539/jmr.v11n5p11
  4. [4] Bae, J. U. N. Y. (1995). A note on fuzzy ideals in BCK-algebras. Mathematica japonicae, 42(2), 333–335. https://cir.nii.ac.jp/crid/1571417124680401792
  5. [5] Jun, Y. B. (1999). Characterizations of Noetherian BCK-algebras via fuzzy ideals. Fuzzy sets and systems, 108(2), 231–234. https://doi.org/10.1016/S0165-0114(97)00329-1
  6. [6] Jun, Y. B. (1997). Finite valued fuzzy ideals in BCK-algebras. Journal of fuzzy mathematics, 5, 111–114.
  7. [7] Rasuli, R. (2022). t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras. Mathematical analysis and its contemporary applications, 4(2), 17–34. https://doi.org/10.30495/maca.2021.1942817.1034
  8. [8] Madhavi, U. B., Sree, V. J., Ramesh, D., & Satyanarayana, B. (2019). Intuitionistic Fuzzy Translations of Implicative Ideals of BCK-Algebra. Gujarat research society, 21, 528–533. https://www.researchgate.net/publication/343649897
  9. [9] Naik, K. A., Satyanarayana, B., Ramesh, D., & Krishna, B. T. (2026). Interval-valued neutrosophic fuzzy n-fold positive implicative ideals of BCK-algebras: Properties and characterizations. Neutrosophic sets and systems, 95(1), 341-358. https://doi.org/10.5281/zenodo.17088824
  10. [10] Sree, V. J., & Satyanarayana, B. (2020). Derivations of intuitionistic fuzzy subimplicative ideals of BCK-algebras. International journal of innovative science engineering and technology (IJISET), 29, 1478–1489. https://www.mililink.com/upload/article/1105441036aams_vol_206_april_2021_a15_p1147-1166_b._satyanarayana_and_u._bindu_madhavi.pdf
  11. [11] Satyanarayana, B., Madhavi, U. B., & Prasad, R. D. (2010). On foldness of intuitionistic fuzzy h-ideals in bck-algebras. International mathematical forum, 5(45), 2205–2221. https://www.researchgate.net/publication/268658362
  12. [12] Kalavath, A. N., & Bavanari, S. (2025). (T, S)-norms over intuitionistic fuzzy implicative and positive implicative ideals in BCK-algebra. https://doi.org/10.48313/uda.vi.76
  13. [13] Abu Osman, M. T. (1987). On some product of fuzzy subgroups. Fuzzy sets and systems, 24(1), 79–86. https://doi.org/10.1016/0165-0114(87)90115-1
  14. [14] Iséki, K., & Tanaka, S. (1978). An introduction to the theory of the BCK-algebras. Mathematica Japonica, 23(1), 1–26. https://cir.nii.ac.jp/crid/1570572699731866880
  15. [15] Jun, Y. B., & Roh, E. H. (1994). Fuzzy commutative ideals of BCK-algebras. Fuzzy sets and systems, 64(3), 401–405. https://doi.org/10.1016/0165-0114(94)90163-5
  16. [16] Meng, J. (1994). On ideals in BCK-algebras. Math. japon, 40, 143–154.

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Published

2024-03-13

Issue

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

Section

Articles

How to Cite

Satyanarayana, B., & Kalavath, A. N. (2024). (T, S)-norms over intuitionistic fuzzy implicative and positive implicative ideals in BCK-algebra. Uncertainty Discourse and Applications, 1(1), 29-40. https://doi.org/10.48313/uda.vi.76

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