New approach to bisemiring theory via the bipolar valued neutrosophic normal sets

In this paper, we introduce the notion of bipolar-valued neutrosophic subbisemiring (BVNSBS), level sets of BVNSBS, and bipolar valued neutrosophic normal subbisemiring (BVNNSBS) of a bisemiring. The concept of BVNSBS is a new generalization of subbisemiring over bisemirings. We discussed the theory of ([xi], [tau])-BVNSBS and ([xi], [tau])-BVNNSBS over bisemirings and presented several illustrative examples to demonstrate the sufficiency and validity of the proposed theorems, lemmas, and propositions. Keywords: Fuzzy set; Bipolar valued neutrosophic subbisemiring; Bipolar valued neutrosophic bisemiring; Homomorphism; Normal.