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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 25 , Issue 2 , PP: 325-337, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups

A. Rajalakshmi 1 , Nasreen Kausar 2 , Brikena Vrioni 3 * , K. Lenin Muthu Kumaran 4 , Nezir Aydin 5 , Murugan Palanikumar 6

  • 1 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, 606603, India - (pearlakshmi03@gmail.com)
  • 2 Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Istanbul, Turkey - (kausar.nasreen57@gmail.com)
  • 3 School of Arts and Sciences, American International University, Kuwait - (Brikena.vrioni@yahoo.com)
  • 4 Department of Mathematics, Shanmuga Industries Arts and Science College, Affiliated to Thiruvalluvar University, Tiruvannamalai, Tamil Nadu, 606603, India - (leninmuthukumaran@gmail.com)
  • 5 College of Science and Engineering Hamad Bin Khalifa University, 34110 Doha, Qatar; Department of Industrial Engineering, Yildiz Technical University, Besiktas, 34349, Istanbul, Turkey - (naydin@hbku.edu.qa)
  • 6 Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India - (palanimaths86@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.250228

    Received: January 10, 2024 Revised: March 16, 2024 Accepted: April 17, 2024
    Abstract

    In this paper, we introduce the notion of $\flat,\ell$-neutrosophic subsemigroup (NSS), neutrosophic left ideal(NLI), neutrosophic right ideal(NRI), neutrosophic ideal (NI), neutrosophic bi-ideal(NBI), $(\epsilon, \epsilon \vee q)$-neutrosophic ideal, neutrosophic bi-ideal of an ordered $\Gamma$-semigroups and discuss some of their properties. The concept of $\flat,\ell$-neutrosophic ideal is a new extension of neutrosophic ideal over ordered $\Gamma$-semigroups $\mathcal{Z}$. A non-empty subset $\xi_{\flat}$ is a $(\flat, \ell)$-NSS (NLI, NRI, NBI, (1,2)-ideal) of $\mathcal{Z}$. Then the lower level set $\Delta_{\flat}$ is an subsemigroup $(LI, RI, BI, (1,2)-ideal)$ of $\mathcal{Z}$, where $\Delta_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)> \flat\}$, $\Psi_{\flat}=\{\varrho\in \mathcal{Z} |\Delta(\varrho)> \flat\}$ and $\mho_{\flat}=\{\varrho\in \mathcal{Z}|\Delta(\varrho)< \flat\}$. A subset $\xi=[\Delta,\Psi,\mho]$ is a $(\flat, \ell)- NSS[NLI,NRI,NBI,(1, 2)-ideal]$ of $\mathcal{Z}$ if and only if each non-empty level subset $\xi_{t}$ is a subsemigroup $[LI,RI,BI,(1,2)-ideal]$ of $\mathcal{Z}$ for all $t\in(\flat, \ell]$. Every $(\epsilon, \epsilon \vee q)$NBI of $\mathcal{Z}$ is a $(\flat,\ell)$NBI of $\mathcal{Z}$, but converse need not be true and examples are provided to illustrate our results.

    Keywords :

    Ordered &Gamma , -semigroups , neutrosophic ideals , bi-ideals , (♭, ℓ) bi-ideals , (ϵ, ϵ &or , q) bi-ideals

    References

    [1] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965), 338-353.

    [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87-96.

    [3] R. R. Yager, Pythagorean membership grades in multi criteria decision-making, IEEE Trans. Fuzzy Systems, 22, (2014), 958-965.

     

    [4] Mahmoud, H. Abdelhafeez, A. ”Spherical Fuzzy Multi-Criteria Decision-Making Approach for Risk Assessment of Natech,” Journal of Neutrosophic and Information Fusion, vol. 2, no. 1, pp. 59-68, 2023.

    [5] Ali, O. Mashhadani, S. Alhakam, I. M., S. ”A New Paradigm for Decision Making under Uncertainty in Signature Forensics Applications based on Neutrosophic Rule Engine,” Journal of International Journal of Neutrosophic Science, vol. 24, no. 2, pp. 268-282, 2024.

    [6] M Palanikumar, N Kausar, H Garg, A Iampan, S Kadry, M Sharaf, Medical robotic engineering selection based on square root neutrosophic normal interval-valued sets and their aggregated operators, AIMS Mathematics, 8(8), (2023), 17402–17432.

    [7] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani and T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, Journal of Intelligent and Fuzzy Systems, 36, (2019), 2829-284.

    [8] Rosenfeld, Fuzzu groups, J.Math. Anal. Appl.35 (1971) 512-517.

    [9] N. Kuroki, On fuzzy semigroups, Inform. Sci. 53 (1991), 203-236.

    [10] J. N. Mordeson, D. S. Malik, N. Kuroki, Fuzzy semigroups, springer-Verlag Berlin Heidelberg GmbH, 2003.

    [11] M. K. Sen, On Γ-semigroups, Proceedings of International conference on Algebra and its Application Decker publication, New yark, (1981), 301.

    [12] M. K. Sen and N. K Saha, On Γ-semigroup, I, Bull.Calcutta Math. Soc.,(1986), 78 180-186.

    [13] N.Kehayopula, On ordered Γ-semigroups, Scientiae Mathematicae Japonicae Online, e-2010, 37-43.

    [14] Somsak Lekkoksung, On Q-fuzzy ideals in ordered semigroups, International Journal of Pure and Applied Mathematics,92(3) (2014), 369–379.

    [15] N.Kehayopula and Tsingelis, Fuzzy sets in ordered groupoids, semigroup Forum, 65, (2005) 128-132 .

    [16] F. M. Khan, N. H. Sarmin and A. Khan. Some new characterization of ordered semigroups in terms of (λ, θ)-fuzzy bi-ideals, International Journal of Algebra and Statistics, 1(1)(2012), 22–32.

    [17] Y. B. Jun, Asghar Khan and Muhammad Shabir, Ordered Semigroups Characterized by Their (ϵ, ϵ,∨q)- Fuzzy Bi-Ideals, Bull. Malays. Math. Sci. Soc. (2) 32(3) (2009), 391-408.

    [18] S. K. Bhakat P. DaS. (ϵ, ϵ,∨q)-Fuzzy subsemigroup. Fuzzy Sets and Systems, 80(3)(1996), 359–368.

    [19] O. Kazanci and S. Yamak, Generalized fuzzy bi-ideals of semigroup, Soft Computing, 12 (2008), 1119- 1124.

    [20] F. Smarandache, A unifying field in logics Neutrosophy Neutrosophic Probability, Set and Logic, Rehoboth American Research Press (1999).

    [21] Ozcek, M. ”A Review on the Structure of Fuzzy Regular Proper Mappings in Fuzzy Topological Spaces and Their Properties,” Journal of Pure Mathematics for Theoretical Computer Science, vol. 3, no. 2, pp. 60-71, 2023.

    [22] Palanikumar M, Selvi G, Ganeshsree Selvachandran and Tan S.L, New approach to bisemiring theory via the bipolar-valued neutrosophic normal sets, Neutrosophic Sets and Systems, 55, 427-450, 2023.

    [23] K. Hila and E. Pisha. On bi-ideals on ordered Γ-semigroups. Hacettepe Journal of Mathematics and Statistics, 40(6), (2011), 793-804.

    Cite This Article As :
    Rajalakshmi, A.. , Kausar, Nasreen. , Vrioni, Brikena. , Lenin, K.. , Aydin, Nezir. , Palanikumar, Murugan. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. Kausar, N. Vrioni, B. Lenin, K. Aydin, N. Palanikumar, M. (2025). Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science, (), 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A.. Kausar, Nasreen. Vrioni, Brikena. Lenin, K.. Aydin, Nezir. Palanikumar, Murugan. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science , no. (2025): 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. , Kausar, N. , Vrioni, B. , Lenin, K. , Aydin, N. , Palanikumar, M. (2025) . Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science , () , 325-337 . DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi A. , Kausar N. , Vrioni B. , Lenin K. , Aydin N. , Palanikumar M. [2025]. Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups. International Journal of Neutrosophic Science. (): 325-337. DOI: https://doi.org/10.54216/IJNS.250228
    Rajalakshmi, A. Kausar, N. Vrioni, B. Lenin, K. Aydin, N. Palanikumar, M. "Characterization of various (b,l) neutrosophic ideals of an ordered Gamma semigroups," International Journal of Neutrosophic Science, vol. , no. , pp. 325-337, 2025. DOI: https://doi.org/10.54216/IJNS.250228

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