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Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making

Author

Listed:
  • Tahir Mahmood

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Ubaid Ur Rehman

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Abdul Jaleel

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Jabbar Ahmmad

    (Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan)

  • Ronnason Chinram

    (Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand)

Abstract

This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union, intersection, extended intersection, and related properties. The OR and AND operations for bipolar complex fuzzy soft set are also initiated in this study. Moreover, this study contains the decision-making algorithm and real-life examples to display the success and usability of bipolar complex fuzzy soft sets. Finally, the comparative study of initiated notions with some prevailing ideas are also interpreted in this study.

Suggested Citation

  • Tahir Mahmood & Ubaid Ur Rehman & Abdul Jaleel & Jabbar Ahmmad & Ronnason Chinram, 2022. "Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1048-:d:778789
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    References listed on IDEAS

    as
    1. Tahir Mahmood & Ali Jaballah, 2020. "A Novel Approach towards Bipolar Soft Sets and Their Applications," Journal of Mathematics, Hindawi, vol. 2020, pages 1-11, October.
    2. Ronnason Chinram & Tahir Mahmood & Ubaid Ur Rehman & Zeeshan Ali & Aiyared Iampan & Sami Ullah Khan, 2021. "Some Novel Cosine Similarity Measures Based on Complex Hesitant Fuzzy Sets and Their Applications," Journal of Mathematics, Hindawi, vol. 2021, pages 1-20, January.
    3. Muhammad Akram & Maria Shabir & Ahmad N. Al-Kenani & José Carlos R. Alcantud & Sami Ullah Khan, 2021. "Hybrid Decision-Making Frameworks under Complex Spherical Fuzzy N-Soft Sets," Journal of Mathematics, Hindawi, vol. 2021, pages 1-46, March.
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    Citations

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    Cited by:

    1. Xiaopeng Yang & Tahir Mahmood & Ubaid ur Rehman, 2022. "Bipolar Complex Fuzzy Subgroups," Mathematics, MDPI, vol. 10(16), pages 1-17, August.

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