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International Journal of Neutrosophic Science
Volume 23 , Issue 4, PP: 272-292 , 2024 | Cite this article as | XML | Html |PDF

Title

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)

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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 :
Style #
MLA S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari. "New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring." International Journal of Neutrosophic Science, Vol. 23, No. 4, 2024 ,PP. 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
APA S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari. (2024). New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
Chicago S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari. "New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring." Journal of International Journal of Neutrosophic Science, 23 no. 4 (2024): 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
Harvard S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari. (2024). New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
Vancouver S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari. New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 4 ): 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
IEEE S. Selvaraj, Gharib Gharib, Abdallah Al-Husban, Maha Al Soudi, K. Lenin Muthu K., Murugan Palanikumar, K. Sundareswari, New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 4 , (2024) : 272-292 (Doi   :  https://doi.org/10.54216/IJNS.230421)
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