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## 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 Ã 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 Ã be an IVNSBS  of a bisemiring S and V be the strongest interval valued neutrosophic relation (SIVNR) of S.  Prove that Ã 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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