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A New Approach of Complex Fuzzy Ideals in BCK/BCI-Algebras

Author

Listed:
  • Manivannan Balamurugan

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
    These authors contributed equally to this work.)

  • Thukkaraman Ramesh

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
    Department of Mathematics, Sri Vidya Mandir Arts & Science College (Autonomous), Uthangarai 636 902, India
    These authors contributed equally to this work.)

  • Anas Al-Masarwah

    (Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan)

  • Kholood Alsager

    (Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia)

Abstract

The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple differences, and bounded differences of complex fuzzy ideals within BCK/BCI-algebras. Finally, we generate a computer programming algorithm that implements our complex fuzzy subalgebras/ideals in BCK/BCI-algebras procedure for ease of lengthy calculations.

Suggested Citation

  • Manivannan Balamurugan & Thukkaraman Ramesh & Anas Al-Masarwah & Kholood Alsager, 2024. "A New Approach of Complex Fuzzy Ideals in BCK/BCI-Algebras," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1583-:d:1397386
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    References listed on IDEAS

    as
    1. Yingying Xu & Haifeng Song & Lei Du & Songsong Dai & Lazim Abdullah, 2022. "Complex-Valued Migrativity of Complex Fuzzy Operations," Journal of Mathematics, Hindawi, vol. 2022, pages 1-6, April.
    2. Haifeng Song & Lvqing Bi & Bo Hu & Yingying Xu & Songsong Dai, 2021. "New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, March.
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