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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 23 , Issue 2 , PP: 156-173, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms

Satyanarayana B. 1 * , Rajani P. 2 , Ramesh D. 3 , Ahmed Abdelhafeez 4 , Abdelrhman Refaat 5 , Khaled ELMenshawy 6

  • 1 MathematicsDepartment, Acharya Nagarjuna University, Nagarjuna Nagar, India - (drbsn63@yahoo.co.in)
  • 2 BS & H Department, SR Gudlavalleru Engineering College, Gudlavalleru, India - (rajanipapers@gmail.com)
  • 3 Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaih Educational Foundation, Vaddeswaram-522302, Guntur(DT), Andhra Pradesh, India - (ram.fuzzy@gmail.com)
  • 4 Faculty of Information Systems and Computer Science, October 6th University, Giza, 12585, Egypt - (aahafeez.scis@o6u.edu.eg)
  • 5 Faculty of Informatics, Midocean University by Everyone's Smart University, 3999, Fujairah, United Arab Emirates - (abdelrhman.refaat@midocean.ae)
  • 6 Faculty of Information Systems and Computer Science, October 6th University, Giza, 12585, Egypt; Faculty of Informatics, Midocean University by Everyone's Smart University, 3999, Fujairah, United Arab Emirates - (Kmensh.csis@o6u.edu.eg)

    • Doi: https://doi.org/10.54216/IJNS.230213

    Received: June 19, 2023 Revised: September 12, 2023 Accepted: December 27, 2023
    Abstract

    The foundational concepts of subalgebra, ideal, and homomorphism within the domain of BF-algebra were originally introduced by Andrzej Walendziak [A. Walendziak, On BF-Algebras, Math. Slovaca, 57(2) (2007), 119-128]. In this paper, we introduce innovative concepts related to Neutrosophic BF-Subalgebras and Neutrosophic BF-Ideals derived from the application of Subalgebra, Ideal, and Homomorphism principles to Neutrosophic sets. We explore the outcomes concerning a Neutrosophic BF-Ideal with respect to principle of homomorphism, homomorphic image of a Neutrosophic BF-Ideal satisfying the sup-inf property, and homomorphic pre-images within the context of a Neutrosophic set embedded in BF-algebra. The outcomes of the above study are equally applicable to Neutrosophic BF-Subalgebra Lastly, we delve into the conceptual understanding of a level set of a Neutrosophic BF-Ideal within a BF-algebra. In the future, the above study can be extended to address various types of implicative ideals and filters within BF-algebra. Moreover, these Neutrosophic BF-Subalgebras and Neutrosophic BF-Ideals can be applied to neutrosophic soft sets within the context of BF-algebra, which are used for various decision making techniques.

    Keywords :

    BF-algebra , Ideals , Subalgebras , Homomorphism , Neutrosophic BF-Subalgebra , Neutrosophic BF-Ideal.

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    Cite This Article As :
    B., Satyanarayana. , P., Rajani. , D., Ramesh. , Abdelhafeez, Ahmed. , Refaat, Abdelrhman. , ELMenshawy, Khaled. Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 156-173. DOI: https://doi.org/10.54216/IJNS.230213
    B., S. P., R. D., R. Abdelhafeez, A. Refaat, A. ELMenshawy, K. (2024). Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms. International Journal of Neutrosophic Science, (), 156-173. DOI: https://doi.org/10.54216/IJNS.230213
    B., Satyanarayana. P., Rajani. D., Ramesh. Abdelhafeez, Ahmed. Refaat, Abdelrhman. ELMenshawy, Khaled. Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms. International Journal of Neutrosophic Science , no. (2024): 156-173. DOI: https://doi.org/10.54216/IJNS.230213
    B., S. , P., R. , D., R. , Abdelhafeez, A. , Refaat, A. , ELMenshawy, K. (2024) . Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms. International Journal of Neutrosophic Science , () , 156-173 . DOI: https://doi.org/10.54216/IJNS.230213
    B. S. , P. R. , D. R. , Abdelhafeez A. , Refaat A. , ELMenshawy K. [2024]. Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms. International Journal of Neutrosophic Science. (): 156-173. DOI: https://doi.org/10.54216/IJNS.230213
    B., S. P., R. D., R. Abdelhafeez, A. Refaat, A. ELMenshawy, K. "Unveiling Neutrosophic Dimensions in the context of BF-algebras: Investigating Subalgebras, Ideals, and Homomorphisms," International Journal of Neutrosophic Science, vol. , no. , pp. 156-173, 2024. DOI: https://doi.org/10.54216/IJNS.230213

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