674 635
Full Length Article
International Journal of Neutrosophic Science
Volume 19 , Issue 1, PP: 116-131 , 2022 | Cite this article as | XML | Html |PDF

Title

Interval Valued Neutrosophic Subbisemirings of Bisemirings

  M. Palanikumar 1 * ,   K. Arulmozhi 2 ,   Aiyared Iampan 3

1  Department of Advanced Mathematical Science, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India
    (palanimaths86@gmail.com)

2  Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India
    (arulmozhiems@gmail.com)

3  Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand
    (aiyared.ia@up.ac.th)


Doi   :   https://doi.org/10.54216/IJNS.190109

Received: March 08, 2022 Accepted: September 16, 2022

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 :

IVNSBS; IVNNSBS; SIVNR; homomorphism

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 as :
Style #
MLA M. Palanikumar, K. Arulmozhi, Aiyared Iampan. "Interval Valued Neutrosophic Subbisemirings of Bisemirings." International Journal of Neutrosophic Science, Vol. 19, No. 1, 2022 ,PP. 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)
APA M. Palanikumar, K. Arulmozhi, Aiyared Iampan. (2022). Interval Valued Neutrosophic Subbisemirings of Bisemirings. Journal of International Journal of Neutrosophic Science, 19 ( 1 ), 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)
Chicago M. Palanikumar, K. Arulmozhi, Aiyared Iampan. "Interval Valued Neutrosophic Subbisemirings of Bisemirings." Journal of International Journal of Neutrosophic Science, 19 no. 1 (2022): 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)
Harvard M. Palanikumar, K. Arulmozhi, Aiyared Iampan. (2022). Interval Valued Neutrosophic Subbisemirings of Bisemirings. Journal of International Journal of Neutrosophic Science, 19 ( 1 ), 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)
Vancouver M. Palanikumar, K. Arulmozhi, Aiyared Iampan. Interval Valued Neutrosophic Subbisemirings of Bisemirings. Journal of International Journal of Neutrosophic Science, (2022); 19 ( 1 ): 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)
IEEE M. Palanikumar, K. Arulmozhi, Aiyared Iampan, Interval Valued Neutrosophic Subbisemirings of Bisemirings, Journal of International Journal of Neutrosophic Science, Vol. 19 , No. 1 , (2022) : 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)