International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 19 , Issue 1 , PP: 116-131, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

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 :
    Palanikumar, M.. , Arulmozhi, K.. , Iampan, Aiyared. Interval Valued Neutrosophic Subbisemirings of Bisemirings. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 116-131. DOI: https://doi.org/10.54216/IJNS.190109
    Palanikumar, M. Arulmozhi, K. Iampan, A. (2022). Interval Valued Neutrosophic Subbisemirings of Bisemirings. International Journal of Neutrosophic Science, (), 116-131. DOI: https://doi.org/10.54216/IJNS.190109
    Palanikumar, M.. Arulmozhi, K.. Iampan, Aiyared. Interval Valued Neutrosophic Subbisemirings of Bisemirings. International Journal of Neutrosophic Science , no. (2022): 116-131. DOI: https://doi.org/10.54216/IJNS.190109
    Palanikumar, M. , Arulmozhi, K. , Iampan, A. (2022) . Interval Valued Neutrosophic Subbisemirings of Bisemirings. International Journal of Neutrosophic Science , () , 116-131 . DOI: https://doi.org/10.54216/IJNS.190109
    Palanikumar M. , Arulmozhi K. , Iampan A. [2022]. Interval Valued Neutrosophic Subbisemirings of Bisemirings. International Journal of Neutrosophic Science. (): 116-131. DOI: https://doi.org/10.54216/IJNS.190109
    Palanikumar, M. Arulmozhi, K. Iampan, A. "Interval Valued Neutrosophic Subbisemirings of Bisemirings," International Journal of Neutrosophic Science, vol. , no. , pp. 116-131, 2022. DOI: https://doi.org/10.54216/IJNS.190109