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International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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International Journal of Neutrosophic Science

Volume 23 , Issue 4 , PP: 272-292, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring

S. Selvaraj 1 , Gharib Gharib 2 , Abdallah Al-Husban 3 , Maha Al Soudi 4 , K. Lenin Muthu K. 5 , Murugan Palanikumar 6 , K. Sundareswari 7

  • 1 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, India, 606603. - (selvarajindian14@gmail.com)
  • 2 Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan. - (ggharib@zu.edu.jo)
  • 3 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan - (dralhosban@inu.edu.jo)
  • 4 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan - (M alsoudi@asu.edu.jo)
  • 5 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, India, 606603. - (leninmuthukumaran@gmail.com)
  • 6 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (palanimaths86@gmail.com)
  • 7 Department of Mathematics, Al- Ameen Engineering College, Erode. - (sundarimaths@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.230421

    Received: June 11, 2023 Revised: January 15, 2024 Accepted: February 13, 2024
    Abstract

    We introduce the concept of an interval-valued neutrosophic cubic vague subbisemiring (IVNCVSBS), level sets of IVNCVSBS of a bisemiring. IVNCVSBSs are the new extension of neutrosophic subbisemirings and SBS over bisemirings. Let ℵ be a neutrosophic vague subset in $X$, we show that ℶ is a IVNCVSBS of X if and only if all non-empty level set is a SBS of X. Let ℵ be a IVNCVSBS of a bisemiring X and strongest cubic neutrosophic vague relation of X, we prove that ℵ is a IVNCVSBS of X × X. Let ℵ be any IVNCVSBS of X, prove that pseudo cubic neutrosophic vague coset is a IVNCVSBS of X. Let ℵ1, ℵ2,..., ℵn be the family of IVNCVSBS of X1, X2,..., Xn respectively. The homomorphic image of every IVNCVSBS is an IVNCVSBS. The homomorphic pre-image of every IVNCVSBS is an IVNCVSBS. Examples are provided to strengthen our results.

    Keywords :

    subbisemiring , cubic neutrosophic subbisemiring , vague bisemiring , homomorphism.

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    Cite This Article As :
    Selvaraj, S.. , Gharib, Gharib. , Al-Husban, Abdallah. , Al, Maha. , Lenin, K.. , Palanikumar, Murugan. , Sundareswari, K.. New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 272-292. DOI: https://doi.org/10.54216/IJNS.230421
    Selvaraj, S. Gharib, G. Al-Husban, A. Al, M. Lenin, K. Palanikumar, M. Sundareswari, K. (2024). New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. International Journal of Neutrosophic Science, (), 272-292. DOI: https://doi.org/10.54216/IJNS.230421
    Selvaraj, S.. Gharib, Gharib. Al-Husban, Abdallah. Al, Maha. Lenin, K.. Palanikumar, Murugan. Sundareswari, K.. New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. International Journal of Neutrosophic Science , no. (2024): 272-292. DOI: https://doi.org/10.54216/IJNS.230421
    Selvaraj, S. , Gharib, G. , Al-Husban, A. , Al, M. , Lenin, K. , Palanikumar, M. , Sundareswari, K. (2024) . New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. International Journal of Neutrosophic Science , () , 272-292 . DOI: https://doi.org/10.54216/IJNS.230421
    Selvaraj S. , Gharib G. , Al-Husban A. , Al M. , Lenin K. , Palanikumar M. , Sundareswari K. [2024]. New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. International Journal of Neutrosophic Science. (): 272-292. DOI: https://doi.org/10.54216/IJNS.230421
    Selvaraj, S. Gharib, G. Al-Husban, A. Al, M. Lenin, K. Palanikumar, M. Sundareswari, K. "New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring," International Journal of Neutrosophic Science, vol. , no. , pp. 272-292, 2024. DOI: https://doi.org/10.54216/IJNS.230421

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