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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 1 , PP: 51-64, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Interval Valued Neutrosophic Subalgebra in INK-Algebra

R. Rajakumari 1 * , KR. Balasubramanian 2 , A. Vadivel 3

  • 1 Department of Mathematics, H. H. The Rajah’s college, Affiliated by Bharathidasan University, Tiruchirappalli, Pudukkottai-622-001, Tamil Nadu, India. - (rajiboomi1986@gmail.com)
  • 2 Department of Mathematics, H. H. The Rajah’s college, Affiliated by Bharathidasan University, Tiruchirappalli, Pudukkottai-622-001, Tamil Nadu, India. - (balamohitha@gmail.com)
  • 3 Arignar Anna Government Arts College, Namakkal - 637 002, India; Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India. - (avmaths@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.240105

    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

    [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] 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. 

    Cite This Article As :
    Rajakumari, R.. , Balasubramanian, KR.. , Vadivel, A.. Interval Valued Neutrosophic Subalgebra in INK-Algebra. International Journal of Neutrosophic Science, vol. , no. , 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, (), 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 , no. (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 , () , 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. (): 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, vol. , no. , pp. 51-64, 2024. DOI: https://doi.org/10.54216/IJNS.240105

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