Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring

Abstract

The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic characteristics and important properties of CIVNSBS. We propose the level sets of CIVNSBS and complex interval valued neutrosophic normal subbisemiring (CIVNNSBS) of bisemirings. Moreover, we introduce CIVNNSBS of bisemiring. Let ¡ be a complex neutrosophic subset of bisemiring S. Then is a CIVNSBS of S if and only if all non empty level set is a subbisemiring, where . Let ¡be a CIVNSBS of bisemiring S and V be the strongest complex neutrosophic relation of bisemiring S. Then ¡ is a CIVNSBS of bisemiring S if and only if V is a CIVNSBS of . We illustrate that homomorphic images of every CIVNSBS is a CIVNSBS and homomorphic pre-images of every CIVNSBS is a CIVNSBS. Examples are provided to illustrate our results.\\