Volume 19 • Issue 1 • PP: 116-131 • 2022
Interval Valued Neutrosophic Subbisemirings of Bisemirings
View PDF Abstract
We introduce the notion of interval valued neutrosophic subbisemirings (IVNSBSs), level sets of IVNSBSs and interval valued neutrosophic normal subbisemirings (IVNNSBSs) of bisemirings. Also, we introduce an approach to (α , β)-IVNSBSs and IVNNSBSs over bisemirings. Let à be an interval valued neutrosophic set (IVN set) in a bisemiring S. We have proved that š = (sTA‚ sIA‚ sFA) is an IVNSBS of S if and only if all non-void level set S(T,S) is a subbisemiring of S for t, s ∈ [[0,1]]. Let à be an IVNSBS of a bisemiring S and V be the strongest interval valued neutrosophic relation (SIVNR) of S. Prove that à is an IVNSBS of S if and only if V is an IVNSBS of S X S. We illustrate homomorphic image of IVNSBS is an IVNSBS. We find that homomorphic preimage of IVNSBS is an IVNSBS. Examples are provided to illustrate our results.
Keywords
References
[1] J. Ahsan, K. Saifullah, F. Khan, Fuzzy semirings, Fuzzy Sets and systems, vol. 60, pp. 309--320,
1993.
[2] M. Al-Tahan, B. Davvaz, M. Parimala, A note on single valued neutrosophic sets in ordered
groupoids, International Journal of Neutrosophic Science, vol. 10, no. 2, pp. 73--83, 2020.
[3] K. Arulmozhi, The algebraic theory of semigroups and semirings, Lap Lambert Academic
Publishing, Mauritius, 2019.
[4] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their
applications in multi-attribute decision making problems, Journal of Intelligent and Fuzzy
Systems, vol. 36, pp. 2829--2844, 2019.
[5] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87--96,
1986.
[6] B. C. Cuong, V. Kreinovich, Picture fuzzy sets a new concept for computational intelligence
problems, Proceedings of 2013 Third World Congress on Information and Communication
Technologies (WICT 2013), IEEE, pp. 1--6, 2013.
[7] S. J. Golan, Semirings and their applications, Kluwer Academic Publishers, London, 1999.
[8] F. Hussian, R. M. Hashism, A. Khan, M. Naeem, Generalization of bisemirings, International
Journal of Computer Science and Information Security, vol. 14, no. 9, pp. 275--289, 2016.
[9] A. Iampan, P. Jayaraman, S. D. Sudha, N. Rajesh, Interval-valued neutrosophic ideals of Hilbert
algebras, International Journal of Neutrosophic Science, vol. 18, no. 4, pp. 223--237, 2022.
[10] Iampan, P. Jayaraman, S. D. Sudha, N. Rajesh, Interval-valued neutrosophic subalgebras of
Hilbert algebras, Asia Pacific Journal of Mathematics, vol. 9, Article no. 16, 2022.
[11] L. Jagadeeswari, V. J. Sudhakar, V. Navaneethakumar, S. Broumi, Certain kinds of bipolar
interval valued neutrosophic graphs, International Journal of Neutrosophic Science, vol. 16, no.
1, pp. 49--61, 2021.
[12] M. Palanikumar, K. Arulmozhi, On various ideals and its applications of bisemirings,
Gedrag and Organisatie Review, vol. 33, no, 2, pp. 522--533, 2020.
[13] M. Palanikumar, K. Arulmozhi, On intuitionistic fuzzy normal subbisemirings of
bisemirings, Nonlinear Studies, vol. 28, no. 3, pp. 717--721, 2021.
[14] M. Palanikumar, K. Arulmozhi, On new ways of various ideals in ternary semigroups,
Matrix Science Mathematic, vol. 4, no. 1, pp. 6--9, 2020.
[15] M. Palanikumar, K. Arulmozhi, $(\alpha, \beta)$-Neutrosophic subbisemiring of bisemiring,
Neutrosophic Sets and Systems, vol. 48, pp. 368--385, 2022.
[16] M. Palanikumar, K. Arulmozhi, On various tri-ideals in ternary semirings, Bulletin of the
International Mathematical Virtual Institute, vol. 11, no. 1, pp. 79--90, 2021.
[17] M. Palanikumar, K. Arulmozhi, On Pythagorean normal subbisemiring of bisemiring,
Annals of Communications in Mathematics, vol. 4, no. 1, pp. 63--72, 2021.
[18] M. Palanikumar, K. Arulmozhi, On various almost ideals of semirings, Annals of
Communications in Mathematics, vol. 4, no. 1, pp. 17--25, 2021.
[19] M. K. Sen, S. Ghosh, An introduction to bisemirings, Asian Bulletin of Mathematics, vol.
28, no. 3, pp. 547--559, 2001.
[20] F. Smarandache, A unifying field in logics. Neutrosophy: neutrosophic probability, set and
logic, American Research Press, Rehoboth, 1999.
[21] R. R. Yager, Pythagorean membership grades in multi criteria decision-making, IEEE
Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 958--965, 2014.
[22] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, no. 3, pp. 338--353, 1965.
Cite This Article
Choose your preferred format