TY - JOUR
T1 - Characterization of various (♭, ℓ) neutrosophic ideals of an ordered Γ-semigroups
AU - Rajalakshmi, A.
AU - Kausar, Nasreen
AU - Vrioni, Brikena
AU - Kumaran, K. Lenin Muthu
AU - Aydin, Nezir
AU - Palanikumar, Murugan
N1 - Publisher Copyright:
© 2025, American Scientific Publishing Group (ASPG). All rights reserved.
PY - 2024/7/27
Y1 - 2024/7/27
N2 - In this paper, we introduce the notion of ♭, ℓ-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), (ϵ, ϵ ∨ q)-neutrosophic ideal, neutrosophic bi-ideal of an ordered Γ-semigroups and discuss some of their properties. The concept of ♭, ℓ-neutrosophic ideal is a new extension of neutrosophic ideal over ordered Γ-semigroups Z. A non-empty subset ξ♭ is a (♭, ℓ)-NSS (NLI, NRI, NBI, (1,2)-ideal) of Z. Then the lower level set ∆♭ is an subsemi-group (LI, RI, BI, (1, 2) − ideal) of Z, where ∆♭ = {ϱ ∈ Z|∆(ϱ) > ♭}, Ψ♭ = {ϱ ∈ Z|∆(ϱ) > ♭} and ℧♭ = {ϱ ∈ Z|∆(ϱ) < ♭}. A subset ξ = [∆, Ψ, ℧] is a (♭, ℓ) − NSS[NLI, NRI, NBI, (1, 2) − ideal] of Z if and only if each non-empty level subset ξt is a subsemigroup [LI, RI, BI, (1, 2) − ideal] of Z for all t ∈ (♭, ℓ]. Every (ϵ, ϵ ∨ q)NBI of Z is a (♭, ℓ)NBI of Z, but converse need not be true and examples are provided to illustrate our results.
AB - In this paper, we introduce the notion of ♭, ℓ-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), (ϵ, ϵ ∨ q)-neutrosophic ideal, neutrosophic bi-ideal of an ordered Γ-semigroups and discuss some of their properties. The concept of ♭, ℓ-neutrosophic ideal is a new extension of neutrosophic ideal over ordered Γ-semigroups Z. A non-empty subset ξ♭ is a (♭, ℓ)-NSS (NLI, NRI, NBI, (1,2)-ideal) of Z. Then the lower level set ∆♭ is an subsemi-group (LI, RI, BI, (1, 2) − ideal) of Z, where ∆♭ = {ϱ ∈ Z|∆(ϱ) > ♭}, Ψ♭ = {ϱ ∈ Z|∆(ϱ) > ♭} and ℧♭ = {ϱ ∈ Z|∆(ϱ) < ♭}. A subset ξ = [∆, Ψ, ℧] is a (♭, ℓ) − NSS[NLI, NRI, NBI, (1, 2) − ideal] of Z if and only if each non-empty level subset ξt is a subsemigroup [LI, RI, BI, (1, 2) − ideal] of Z for all t ∈ (♭, ℓ]. Every (ϵ, ϵ ∨ q)NBI of Z is a (♭, ℓ)NBI of Z, but converse need not be true and examples are provided to illustrate our results.
KW - (ϵ, ϵ ∨ q) bi-ideals
KW - (♭, ℓ) bi-ideals
KW - Ordered Γ-semigroups
KW - bi-ideals
KW - neutrosophic ideals
UR - http://www.scopus.com/inward/record.url?scp=85202739519&partnerID=8YFLogxK
U2 - 10.54216/IJNS.250228
DO - 10.54216/IJNS.250228
M3 - Article
AN - SCOPUS:85202739519
SN - 2692-6148
VL - 25
SP - 325
EP - 337
JO - International Journal of Neutrosophic Science
JF - International Journal of Neutrosophic Science
IS - 2
ER -