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International Journal of Neutrosophic Science
Volume 19 , Issue 1, PP: 116-131 , 2022 | Cite this article as | XML | Html |PDF

Title

Interval Valued Neutrosophic Subbisemirings of Bisemirings

Authors Names :   M. Palanikumar   1 *     K. Arulmozhi   2     Aiyared Iampan   3  

1  Affiliation :  Department of Advanced Mathematical Science, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India

    Email :  palanimaths86@gmail.com


2  Affiliation :  Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India

    Email :  arulmozhiems@gmail.com


3  Affiliation :  Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand

    Email :  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

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Cite this Article as :
M. Palanikumar , K. Arulmozhi , Aiyared Iampan, Interval Valued Neutrosophic Subbisemirings of Bisemirings, International Journal of Neutrosophic Science, Vol. 19 , No. 1 , (2022) : 116-131 (Doi   :  https://doi.org/10.54216/IJNS.190109)