New approach for subbisemiring of bisemiring is applied to complex

cubic anti neutrosophic set and its extension

Aiyared Iampan1,∗, Murugan Palanikumar2

1Department of Mathematics, School of Science, University of Phayao, 19 Moo 2,Tambon Mae Ka, Amphur

Mueang, Phayao 56000, Thailand

2Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical

Sciences, Chennai-602105, India

E-mails: aiyared.ia@up.ac.th; palanimaths86@gmail.com

Abstract

We construct and analyze the concept of complex cubic anti neutrosophic subbisemiring (ComCANSBS). We

analyze the important properties and homomorphic aspects of ComCANSBS. For bisemirings, we propose the

ComCANSBS level sets. A complex neutrosophic subset of bisemiring Ⓢ is represented by the symbol Γ if

and only if each non-empty level set R(℘,κ), where R = (

z}|{

ℜ⊤

Γ ·eiθ

z}|{

ℑ⊤

Γ ,

z}|{

ℜ ג

Γ ·eiθ

z}|{

ℑ ג

Γ ,

z}|{

ℜ𭟋

Γ ·eiθ

z}|{

ℑ𭟋

Γ ,ℜ⊤

Γ ·

eiθℑ⊤

Γ ,ℜ ג

Γ · eiθℑ ג

Γ,ℜ𭟋

Γ · eiθℑ𭟋

Γ ) is a ComCANSBS of Ⓢ. Let Υ be a ComCANSBS of bisemiring Ⓢ. If and

only if Υ is a ComCANSBS of Ⓢ × Ⓢ, then Γ is a ComCANSBS of bisemiring Ⓢ. Let Γ be the strongest

complex anti neutrosophic relation of bisemiring Ⓢ. We show that homomorphic images of all ComCANSBSs

are ComCANSBSs, and homomorphic pre-images of all ComCANSBSs are ComCANSBSs. There are

examples given to illustrate our results.

Keywords: ComCANSBS; ComCNANSBS; SBS; homomorphism