1 Affiliation : Department of Advanced Mathematical Science, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India
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2 Affiliation : Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India
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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
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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.
IVNSBS; IVNNSBS; SIVNR; homomorphism
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