New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring

Abstract

We introduces the concept of a 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 be a neutrosophic vague subset in $X$, we show that is a IVNCVSBS of X if and only if all non empty level set is a SBS of X. Let be a IVNCVSBS of a bisemiring X and strongest cubic neutrosophic vague relation of X, we prove that is a IVNCVSBS of X × X. Let be any IVNCVSBS of X, prove that pseudo cubic neutrosophic vague coset is a IVNCVSBS of X. Let 1, 2,...,n be the family of IVNCVSBS of X1, X2,..., Xn respectively.The homomorphic image of every IVNCVSBS is a IVNCVSBS. The homomorphic pre-image of every IVNCVSBS is a IVNCVSBS. Examples are provided to strengthen our results.