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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.

    References

    [1] Zadeh, L. A.; Fuzzy sets, Information and Control 1965, 8, no. 3, 338-353.

    [2] Gau, W. L.; Buehrer, D. J.; Vague sets, IEEE Transactions on Systems, Man and Cybernetics 1993, 23, no. 2, 610-613.

    [3] Atanassov, K; Intuitionistic fuzzy sets, Fuzzy Sets and Systems 1986, 20, no. 1, 87-96.

    [4] Smarandache, F.; A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability (fourth edition), Rehoboth American Research Press, 2008.

    [5] Smarandache, F.; Neutrosophic set-a generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics 2005, 24, no. 3, 287-297.

    [6] Ahsan, J.; Saifullah, K.; Khan, F. Fuzzy semirings, Fuzzy Sets and systems 1993, 60, 309-320.

    [7] SG Quek, H Garg, G Selvachandran, K Arulmozhi,VIKOR and TOPSIS framework with a truthfuldistance measure for the (t, s)-regulated interval-valued neutrosophic soft set, Soft Computing, 1-27, 2023.

    [8] K Arulmozhi, A Iampan, Multi criteria group decision making based on VIKOR and TOPSIS methods for Fermatean fuzzy soft with aggregation operators, ICIC Express Letters 16 (10), 1129–1138, 2022.

    [9] M Palanikumar, K Arulmozhi, MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets and Systems,, 538-555, 2022.

    [10] Palanikumar, M., Arulmozhi, K, On intuitionistic fuzzy normal subbisemiring of bisemiring, Nonlinear Studies 2021, 28(3), 717–721.

    [11] Sen, M.K.; Ghosh, S.; Ghosh, S. An introduction to bisemirings. Southeast Asian Bulletin of Mathematics, 2004, 28(3), 547-559.

    [12] Biswas, R.; Vague groups, International Journal of Computational Cognition 2006, 4, no. 2, 20-23.

    [13] Golan, S. J; Semirings and their applications, Kluwer Academic Publishers, London, 1999.

    [14] Hussian, F.; Hashism, R. M.; Khan, A.; Naeem, M.; Generalization of bisemirings, International Journal of Computer Science and Information Security 2016, 14, no. 9, 275-289.

    [15] Vandiver, H.S. Note on a simple type of algebra in which the cancellation law of addition does not hold. Bulletin of the American Mathematical Society, 1934, 40(12), 914-920.

    [16] Glazek, K. A guide to the literature on semirings and their applications in mathematics and information sciences. Springer, Dordrecht, Netherlands, 2002.

    [17] Jun, Y.B.; Song, S.Z. Subalgebras and closed ideals of BCH-algebras based on bipolar-valued fuzzy sets. Scientiae Mathematicae Japonicae Online, 2008, 427-437.

    [18] Lee, K.J. Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras. Bulletin of the Malaysian Mathematical Sciences Society, 2009, 32(3), 361-373.

    [19] M Palanikumar, S Broumi, Square root Diophantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making, International Journal of Neutrosophic Science, 4, 2022.

    [20] M Palanikumar, K Arulmozhi, Novel possibility Pythagorean interval valued fuzzy soft set method for a decision making, TWMS J. App. and Eng. Math. V.13, N.1, 2023, pp. 327-340.

    [21] Muhiuddin, G.; Harizavi, H.; Jun, Y.B. Bipolar-valued fuzzy soft hyper BCK ideals in hyper BCK algebras. Discrete Mathematics, Algorithms and Applications, 2020, 12(2), 2050018.

    [22] Zararsz, Z.; Riaz, M. Bipolar fuzzy metric spaces with application. Comp. Appl. Math. 2022, 41(49).

    [23] Selvachandran, G.; Salleh, A.R. Algebraic Hyperstructures of vague soft sets associated with hyperrings and hyperideals. The Scientific World Journal, 2015, 2015, 780121.

    [24] Jun, Y.B.; Kim, H.S.; Lee, K.J. Bipolar fuzzy translations in BCK/BCI-algebras. Journal of the Chungcheong Mathematical Society, 2009, 22(3), 399-408.

    [25] Jun, Y.B.; Park, C.H. Filters of BCH-algebras based on bipolar-valued fuzzy sets. International Mathematical Forum, 2009, 4(13), 631-643.

    [26] Hussain, F. Factor bisemirings. Italian Journal of Pure and Applied Mathematics, 2015, 34, 81-88.

    [27] El.Atik, A. A., Abu-Gdairi, R., Nasef, A. A., Jafari, S., Badr, M. (2023). Fuzzy soft sets and decision making in ideal nutrition. Symmetry, 15(8), 1523.

    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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