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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 24 , Issue 1 , PP: 35-50, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Interval Valued Neutrosophic INK-Ideal Via 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; Arignar Anna Government Arts College, Namakkal - 637 002, India. - (balamohitha@gmail.com)
  • 3 Department of Mathematics, Annamalai University, Annamalai Nagar - 608 002, India. - (avmaths@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.240104

    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.

    Cite This Article As :
    Rajakumari, R.. , Balasubramanian, KR.. , Vadivel, A.. Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. International Journal of Neutrosophic Science, vol. , no. , 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, (), 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 , no. (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 , () , 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. (): 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, vol. , no. , pp. 35-50, 2024. DOI: https://doi.org/10.54216/IJNS.240104

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