Homomorphism of complex neutrosophic set extended to cubic Q

neutrosophic set concept via subbisemiring of bisemirings

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 introduce the concept of complex cubic Q neutrosophic subbisemiring (CCQNSBS) is a new extension

of cubic Q neutrosophic subbisemiring. We examine the characteristics and homomorphic features of CCQNSBS.

We communicate the CCQNSBS level sets for bisemirings. A cubic complex Q neutrosophic subset

Γ of bisemiring S if and only if each non-empty level set R(ℓ,♭), where R = (ΘT

R · eiτΘTI ,ΘI

R · eiτΘII

,ΘFR

·

eiτΘFI

,ΘT

R · eiτΘTI

,ΘI

R · eiτΘII

,ΘFR

· eiτΘFI

) is a CCQNSBS of S. We show that the intersection of all CCQNSBSs

yields a CCQNSBS ofS. If Θ1,Θ2, ...,Θn be the finite collection of CCQNSBSs ofS1,S2, ...,Sn

respectively. Then Θ1 × Θ2 × ... × Θn is a CCQNSBS of S1 ×S2 × ... ×Sn. If F : S1 → S2 is a homomorphism,

then F(Θ(ℓ,♭)) is a subbisemiring of CCQNSBS Ω of S2. Examples are provided to show how our

findings are used.

Keywords: CCQNSBS; CCNQNSBS; SBS; Homomorphism