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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 26 , Issue 3 , PP: 26-48, 2025 | Cite this article as | XML | PDF | Full Length Article

An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras

Anas Al-Masarwah 1 , Manivannan Balamurugan 2 * , Thukkaraman Ramesh 3 , Majdoleen Abuqamar 4 , Maryam Abdullah Alshayea 5

  • 1 Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan - (anas.almasarwah@anu.edu.jo)
  • 2 Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India - (balamurugansvm@gmail.com)
  • 3 Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India; Department of Mathematics, Sri Vidya Mandir Arts & Science College (Autonomous), Uthangarai 636902, Tamil Nadu, India - (ramesh1000.d@gmail.com)
  • 4 Department of Mathematics, Faculty of Science, Jadara University, Irbid 21110, Jordan - (m.abuqamar@jadara.edu.jo)
  • 5 Department of Computer Science, College of Engineering and InformationTechnology, Onaizah Colleges, Al-Qassim 56447, Saudi Arabia - (mmeem514@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.260303

    Received: January 27, 2025 Revised: February 23, 2025 Accepted: March 26, 2025
    Abstract

    A complex linear Diophantine fuzzy (CLDF) set extends a linear Diophantine fuzzy set (LDFS) by handling uncertainty with complex-valued membership degrees within a unit disc. In this paper, we combine the notions of LDFS, BCK-algebra, and complex fuzzy set (CFS) to preface and elaborate the innovative concepts of CLDF subalgebras (CLDF − Subs), CLDF ideals (CLDF − Ids), CLDF implicative ideals (CLDF − IIds), and CLDF positive implicative ideals (CLDF − PIIds) in BCK-algebras, and probe their fundamental characteristics. These new notations of certain kinds of algebraic substructures in BCK-algebras serve as a bridge among CLDFS, crisp set, and BCK-algebra and also demonstrate the influence of the CLDFS on a BCK-algebra. Moreover, we examine some illustrative examples and prevalent features of these innovative notions in detail. Finally, characterizations of these intricate fuzzy structures are given, and related results for ideals, implicative ideals, and positive implicative ideals in the view of CLDFSs are obtained.

    Keywords :

    BCK-algebra , Complex linear Diophantine fuzzy set , Complex linear Diophantine fuzzy sub-algebra , Complex linear Diophantine fuzzy idea

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    Cite This Article As :
    Al-Masarwah, Anas. , Balamurugan, Manivannan. , Ramesh, Thukkaraman. , Abuqamar, Majdoleen. , Abdullah, Maryam. An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 26-48. DOI: https://doi.org/10.54216/IJNS.260303
    Al-Masarwah, A. Balamurugan, M. Ramesh, T. Abuqamar, M. Abdullah, M. (2025). An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras. International Journal of Neutrosophic Science, (), 26-48. DOI: https://doi.org/10.54216/IJNS.260303
    Al-Masarwah, Anas. Balamurugan, Manivannan. Ramesh, Thukkaraman. Abuqamar, Majdoleen. Abdullah, Maryam. An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras. International Journal of Neutrosophic Science , no. (2025): 26-48. DOI: https://doi.org/10.54216/IJNS.260303
    Al-Masarwah, A. , Balamurugan, M. , Ramesh, T. , Abuqamar, M. , Abdullah, M. (2025) . An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras. International Journal of Neutrosophic Science , () , 26-48 . DOI: https://doi.org/10.54216/IJNS.260303
    Al-Masarwah A. , Balamurugan M. , Ramesh T. , Abuqamar M. , Abdullah M. [2025]. An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras. International Journal of Neutrosophic Science. (): 26-48. DOI: https://doi.org/10.54216/IJNS.260303
    Al-Masarwah, A. Balamurugan, M. Ramesh, T. Abuqamar, M. Abdullah, M. "An Investigation of Complex Linear Diophantine Fuzzy Ideals in BCK-Algebras," International Journal of Neutrosophic Science, vol. , no. , pp. 26-48, 2025. DOI: https://doi.org/10.54216/IJNS.260303

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