Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring


Palanikumar M., KAUSAR N., Özbilge E., Ozbilge E.

International Journal of Neutrosophic Science, vol.23, no.4, pp.117-135, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.54216/ijns.230409
  • Journal Name: International Journal of Neutrosophic Science
  • Journal Indexes: Scopus, Applied Science & Technology Source
  • Page Numbers: pp.117-135
  • Keywords: CIVNNSBS, CIVNSBS, homomorphism, SBS
  • Yıldız Technical University Affiliated: Yes

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 (ϱ, σ) CIVNNSBS of bisemiring. Let (Formula Presented) be a complex neutrosophic subset of bisemiring S. Then (Formula Presented) is a CIVNSBS of S if and only if all non empty level set (Formula Presented) is a subbisemiring, where (Formula Presented). Let (Formula Presented) be a CIVNSBS of bisemiring S and (Formula Presented) be the strongest complex neutrosophic relation of bisemiring S. Then (Formula Presented) is a CIVNSBS of bisemiring S if and only if (Formula Presented) is a CIVNSBS of S × S. 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.