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International Journal of Neutrosophic Science

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Online: 2690-6805 Print: 2692-6148
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International Journal of Neutrosophic Science
Full Length Article

Volume 24Issue 1PP: 35-50 • 2024

Interval Valued Neutrosophic INK-Ideal Via INK-Algebra

R. Rajakumari 1* ,
KR. Balasubramanian 2 ,
A. Vadivel 3
1Department of Mathematics, H. H. The Rajah’s college, Affiliated by Bharathidasan University, Tiruchirappalli, Pudukkottai-622-001, Tamil Nadu, India.
2Department of Mathematics, H. H. The Rajah’s college, Affiliated by Bharathidasan University, Tiruchirappalli, Pudukkottai-622-001, Tamil Nadu, India; Arignar Anna Government Arts College, Na
3Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India.
* Corresponding Author.
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Received: August 15, 2023 Revised: December 08, 2023 Accepted: March 17, 2024

Abstract

Based on Zadeh’s notion of interval-valued fuzzy set, we develop in this work the notion of interval-valued neutrosophic INK-ideals (briefly, IV N INK-ideals) in INK-algebra and evaluate some of its properties. We show that all N INK-ideals of INK-algebra A can be realized as IV level INK-ideals of INK-algebra A. We then deduce numerous related results, which are summarized in the abstract.

Keywords

Fuzzy INK-ideal interval valued neutrosophic fuzzy set interval valued neutrosophic INKideal.

References

[1] Imai, Y.; Is´eki, K. On axiom systems of propositional calculi. XIV. Proc. Japan Academy 1996.

[2] Is´eki, K.; Tanaka, T. An introduction to the theory of BCK-algebras. Math. Japonica 1978 Vol 23, pp 1-26.

[3] Kaviyarasu, M.; Indhira, K.; Chandrasekaran, V. M. Introduction on INK-algebras. International Journal of Pure and Applied Mathematics 2017, Vol 115 (9), pp 1-10.

[4] Kaviyarasu, M.; Indhira, K.; Chandrasekaran, V. M.; Jocob Kavikumar, Interval-valued fuzzy subalgebra and fuzzy INK-Ideal in INK-algebra. Advances in Algebra and Analysis, Trends in Mathematics, https://doi.org/10.1007/978-3-030-01120-8 3.

[5] Kaviyarasu, M.; Indhira, K. Fuzzy translation on INK-algebra. Jour of Adv Reserch in Dynamical & Control Systems 2019, Vol 11 (10) (SI), pp 938-943.

[6] Mostafa, S. M. Fuzzy implicative ideal in BCK-algebras. Fuzzy Sets and Systems 1997. https://doi.org/S0168-0114 (96) 00017-6

[7] Neggers, J.; Kim, H. S. On d-algebras. Math. Slovaca 1999, Vol 49, pp 19-26.

[8] Sung Min Hong; Young Bae Jun, Anti fuzzy ideals in BCK-algebras. Kyungpook Math. J. 1998, Vol 38, pp 145-150.

[9] Zadeh, L. A. Fuzzy sets. Information and Control 1965, Vol 8. Available via Dialog https: //doi.org/10.1016/ S0019-99581 (65) 90241-X, cited 30 June 1965.

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Rajakumari, R., Balasubramanian, KR., Vadivel, A.. "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra." International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 1, 2024, pp. 35-50. DOI: https://doi.org/10.54216/IJNS.240104
Rajakumari, R., Balasubramanian, K., Vadivel, A. (2024). Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. International Journal of Neutrosophic Science, Volume 24(Issue 1), 35-50. DOI: https://doi.org/10.54216/IJNS.240104
Rajakumari, R., Balasubramanian, KR., Vadivel, A.. "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra." International Journal of Neutrosophic Science Volume 24, no. Issue 1 (2024): 35-50. DOI: https://doi.org/10.54216/IJNS.240104
Rajakumari, R., Balasubramanian, K., Vadivel, A. (2024) 'Interval Valued Neutrosophic INK-Ideal Via INK-Algebra', International Journal of Neutrosophic Science, Volume 24(Issue 1), pp. 35-50. DOI: https://doi.org/10.54216/IJNS.240104
Rajakumari R, Balasubramanian K, Vadivel A. Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. International Journal of Neutrosophic Science. 2024;Volume 24(Issue 1):35-50. DOI: https://doi.org/10.54216/IJNS.240104
R. Rajakumari, K. Balasubramanian, A. Vadivel, "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra," International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 1, pp. 35-50, 2024. DOI: https://doi.org/10.54216/IJNS.240104
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