Characterization of various (♭, ℓ) neutrosophic ideals of an ordered Γ-semigroups

Rajalakshmi A., KAUSAR N., Vrioni B., Kumaran K. L. M., AYDIN N., Palanikumar M.

International Journal of Neutrosophic Science, cilt.25, sa.2, ss.325-337, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.54216/ijns.250228
  • Dergi Adı: International Journal of Neutrosophic Science
  • Derginin Tarandığı İndeksler: Scopus, Applied Science & Technology Source
  • Sayfa Sayıları: ss.325-337
  • Anahtar Kelimeler: (ϵ, ϵ ∨ q) bi-ideals, (♭, ℓ) bi-ideals, bi-ideals, neutrosophic ideals, Ordered Γ-semigroups
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.