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)
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.
| Style | # |
|---|---|
| MLA | R. Rajakumari, KR. Balasubramanian, A. Vadivel. "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra." International Journal of Neutrosophic Science, Vol. 24, No. 1, 2024 ,PP. 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |
| APA | R. Rajakumari, KR. Balasubramanian, A. Vadivel. (2024). Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |
| Chicago | R. Rajakumari, KR. Balasubramanian, A. Vadivel. "Interval Valued Neutrosophic INK-Ideal Via INK-Algebra." Journal of International Journal of Neutrosophic Science, 24 no. 1 (2024): 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |
| Harvard | R. Rajakumari, KR. Balasubramanian, A. Vadivel. (2024). Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |
| Vancouver | R. Rajakumari, KR. Balasubramanian, A. Vadivel. Interval Valued Neutrosophic INK-Ideal Via INK-Algebra. Journal of International Journal of Neutrosophic Science, (2024); 24 ( 1 ): 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |
| IEEE | R. Rajakumari, KR. Balasubramanian, A. Vadivel, Interval Valued Neutrosophic INK-Ideal Via INK-Algebra, Journal of International Journal of Neutrosophic Science, Vol. 24 , No. 1 , (2024) : 35-50 (Doi : https://doi.org/10.54216/IJNS.240104) |