Volume 23 • Issue 4 • PP: 272-292 • 2024
New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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We introduce the concept of an interval-valued neutrosophic cubic vague subbisemiring (IVNCVSBS), level sets of IVNCVSBS of a bisemiring. IVNCVSBSs are the new extension of neutrosophic subbisemirings and SBS over bisemirings. Let ℵ be a neutrosophic vague subset in $X$, we show that ℶ is a IVNCVSBS of X if and only if all non-empty level set is a SBS of X. Let ℵ be a IVNCVSBS of a bisemiring X and strongest cubic neutrosophic vague relation of X, we prove that ℵ is a IVNCVSBS of X × X. Let ℵ be any IVNCVSBS of X, prove that pseudo cubic neutrosophic vague coset is a IVNCVSBS of X. Let ℵ1, ℵ2,..., ℵn be the family of IVNCVSBS of X1, X2,..., Xn respectively. The homomorphic image of every IVNCVSBS is an IVNCVSBS. The homomorphic pre-image of every IVNCVSBS is an IVNCVSBS. Examples are provided to strengthen our results.
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