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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: 51-64 • 2024

Interval Valued Neutrosophic Subalgebra in INK-Algebra

R. Rajakumari 1* ,
KR. Balasubramanian 1 ,
A. Vadivel 2
1Department of Mathematics, H. H. The Rajah’s college, Affiliated by Bharathidasan University, Tiruchirappalli, Pudukkottai-622-001, Tamil Nadu, India.
2Arignar Anna Government Arts College, Namakkal - 637 002, India; Department 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 10, 2023 Revised: December 11, 2023 Accepted: March 19, 2024

Abstract

This work presents the concept of interval-valued neutrosophic INK-subalgebras, also known as IV N INKsubalg’s, which are the level and strong level neutrosophic INK-subalgebras. Next, we establish and validate a few theorems that establish the connection between these concepts and neutrosophic INK-subalgebras. We define the images and inverse images of IV N INK-subalgebras and study the transformations of the homomorphic images and inverse images of interval valud neutrosophic (briefly, IV N) INK-subalgebra into IV N INK-subalgebras.

Keywords

interval valued neutrosophic set neutrosophic INK-subalgebra and interval valued neutrosophic INK-subalgebra.

References

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[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] Kaviyarasu, M.; Indhira, K.; Chandrasekaran, V. M., Neutrosophic set in INK-algebra. Advances in Mathematics: Scientific Journal 2020, Vol 9 (7), pp 4345-4352.

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

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

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

[10] 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 Subalgebra in INK-Algebra." International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 1, 2024, pp. 51-64. DOI: https://doi.org/10.54216/IJNS.240105
Rajakumari, R., Balasubramanian, K., Vadivel, A. (2024). Interval Valued Neutrosophic Subalgebra in INK-Algebra. International Journal of Neutrosophic Science, Volume 24(Issue 1), 51-64. DOI: https://doi.org/10.54216/IJNS.240105
Rajakumari, R., Balasubramanian, KR., Vadivel, A.. "Interval Valued Neutrosophic Subalgebra in INK-Algebra." International Journal of Neutrosophic Science Volume 24, no. Issue 1 (2024): 51-64. DOI: https://doi.org/10.54216/IJNS.240105
Rajakumari, R., Balasubramanian, K., Vadivel, A. (2024) 'Interval Valued Neutrosophic Subalgebra in INK-Algebra', International Journal of Neutrosophic Science, Volume 24(Issue 1), pp. 51-64. DOI: https://doi.org/10.54216/IJNS.240105
Rajakumari R, Balasubramanian K, Vadivel A. Interval Valued Neutrosophic Subalgebra in INK-Algebra. International Journal of Neutrosophic Science. 2024;Volume 24(Issue 1):51-64. DOI: https://doi.org/10.54216/IJNS.240105
R. Rajakumari, K. Balasubramanian, A. Vadivel, "Interval Valued Neutrosophic Subalgebra in INK-Algebra," International Journal of Neutrosophic Science, vol. Volume 24, no. Issue 1, pp. 51-64, 2024. DOI: https://doi.org/10.54216/IJNS.240105
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