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.
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