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Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making

Author

Listed:
  • Manivannan Balamurugan

    (Department of Mathematics, School of Science & Humanities, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India)

  • Nazek Alessa

    (Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Karuppusamy Loganathan

    (Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur 303007, Rajasthan, India)

  • M. Sudheer Kumar

    (Department of Science and Humanities, MLR Institute of Technology, Hyderabad 500043, Telangana, India)

Abstract

In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set.

Suggested Citation

  • Manivannan Balamurugan & Nazek Alessa & Karuppusamy Loganathan & M. Sudheer Kumar, 2023. "Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making," Mathematics, MDPI, vol. 11(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4471-:d:1269432
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    References listed on IDEAS

    as
    1. M. Hamidi & F. Smarandache & Firdous A. Shah, 2021. "Single-Valued Neutro Hyper BCK-Subalgebras," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, September.
    2. G. Muhiuddin & D. Al-Kadi & Lazim Abdullah, 2021. "Bipolar Fuzzy Implicative Ideals of BCK-Algebras," Journal of Mathematics, Hindawi, vol. 2021, pages 1-9, January.
    3. Chiranjibe Jana & Madhumangal Pal, 2018. "Application of Bipolar Intuitionistic Fuzzy Soft Sets in Decision Making Problem," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 7(3), pages 32-55, July.
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