On New Approach Towards Cubic Vague Subbisemirings in Bisemirings

Abstract

From the nature of subbisemiring, we develop a new generalized hybrid structure of vague subbisemiring known as cubic vague subbisemiring (shortly CVSBS). We talk about the CVSBS and level sets CVSBS of bisemiring. At first we define some basic operation such as intersection, cartesian product on them and use these to obtain some of its basic properties under CVSBS. Let L = hA¯L, VLi be the cubic vague subset of S. It is shown that L is a CVSBS if and only if all non empty level set L(α,β) (α, β ∈ D[0, 1]) is a SBS. Let L be the CVSBS and W be the strongest vague relation of S. We show that L is a CVSBS if and only if W is a CVSBS of S × S. After we define homomorphic image and preimage of bisemiring. It will be shown that the homomorphic image and preimage of CVSBS is a CVSBS. To strengthen our results with examples are indicated.