**5. Conclusions**

Several characterizations of the *M*-LTB (RTB) of an ordered Γ-semigroup are described in this article. Our discussion has focused on some of their fundamental characteristics and has also examined some of them using the *M*-tri-ideal generator. We presented the *M*-LTB (RTB) of an ordered Γ-semigroup, which was constructed from an ordered Γ-semigroup element and subset. At the end of our discussion, we explored the relationship between partial order and the *M*-LTB (RTB). In the future, we plan to explore a few more types of tri-basis and tri-*M*-basis. Our study will examine their research on Γ-hyper semigroups using bi-basis and *M*-bi-basis.

**Author Contributions:** Conceptualization, M.P. (M. Palanikumar); methodology, M.P. (Madhumangal Pal); writing original draft, M.P. (M. Palanikumar); conceptualization, C.J.; validation, C.J.; conceptualization, O.A.-S.; review and editing, O.A.-S. and writing—review and editing, M.P. (Madhumangal Pal). All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Informed Consent Statement:** The article does not contain any studies with human participants or animals performed by the author.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors declare that the present work is a joint contribution to this paper and was not supported by any financial and material agency.

**Conflicts of Interest:** The authors declare no conflict of interest.
