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International Journal of Neutrosophic Science
Volume 19 , Issue 4, PP: 37-48 , 2022 | Cite this article as | XML | Html |PDF

Title

Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring

  M. Palanikumar 1 * ,   Aiyared Iampan 2

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  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.190403

Received: May 05, 2022 Accepted: November 10, 2022

Abstract :

We introduce the notion of Diophantine neutrosophic subbisemiring (DioNSBS), level sets of DioNSBS of a bisemiring. The concept of DioNSBS is a generalization of fuzzy subbisemiring over bisemiring. We interact the theory for (λ, μ)-DioNSBS over bisemiring. Let α be the Diophantine neutrosophic subset in S , we show that α = T α , ΞI α , ΞF α ), (Γα, ∆α, Θα) is a DioNSBS of S if and only if all non empty level set α(t,s) is a subbisemiring of S for t, s [0, 1]. Let α be the DioNSBS of a bisemiring S and W be the strongest Diophantine neutrosophic relation of S , we observe that α is a DioNSBS of S if and only if W is a DioNSBS of S × S . Let α1, α2, ..., αn be the family of DioN SBSs of S1, S2, ..., Sn respectively. We show that α1× α2 × ... × αn is a DioNSBS of S1 × S2 × ... × Sn. The homomorphic image of DioNSBS is a DioNSBS. The homomorphic preimage of DioNSBS is a DioNSBS. Examples are provided to illustrate our results.

Keywords :

fuzzy subbisemiring; neutrosophic subbisemiring; Diophantine neutrosophic bisemiring; (λ , μ)-

Diophantine neutrosophic subbisemiring; homomorphism

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Cite this Article as :
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MLA M. Palanikumar, Aiyared Iampan. "Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring." International Journal of Neutrosophic Science, Vol. 19, No. 4, 2022 ,PP. 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)
APA M. Palanikumar, Aiyared Iampan. (2022). Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring. Journal of International Journal of Neutrosophic Science, 19 ( 4 ), 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)
Chicago M. Palanikumar, Aiyared Iampan. "Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring." Journal of International Journal of Neutrosophic Science, 19 no. 4 (2022): 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)
Harvard M. Palanikumar, Aiyared Iampan. (2022). Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring. Journal of International Journal of Neutrosophic Science, 19 ( 4 ), 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)
Vancouver M. Palanikumar, Aiyared Iampan. Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring. Journal of International Journal of Neutrosophic Science, (2022); 19 ( 4 ): 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)
IEEE M. Palanikumar, Aiyared Iampan, Algebraic Structure for (λ, μ)-Diophantine Neutrosophic Bisemiring, Journal of International Journal of Neutrosophic Science, Vol. 19 , No. 4 , (2022) : 37-48 (Doi   :  https://doi.org/10.54216/IJNS.190403)