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Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems

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  • Chaube, Shshank
  • Joshi, Dheeraj Kumar
  • Ujarari, Chandan Singh

Abstract

All the available knowledge related to the Fuzzy Sets (FS) is constricted to express the circumstances when the sum of the degrees of membership and non-membership of any element exceeds one. To keep in mind that in real life there are many ill-defined or too inordinately complex situations, in this article, we propose the concept of Hesitant Bifuzzy Set (HBFS), which appraises Fuzzy Set (FS), Intuitionistic Fuzzy Sets (IFS), Hesitant Fuzzy Set (HFS), Conflicting Bifuzzy Set (CBFS) and Dual Hesitant Fuzzy Set (DHFS) as particular cases. Here we discuss the fundamental operations along with the basic properties of HBFSs. A descriptive example is used to illustrate the proposed concept and method. The supremacy of this study is that all the existing methods only provide the reliability of the system in the form of a fuzzy element while the method introduced in this study always provides a crisp value for the reliability of the system.

Suggested Citation

  • Chaube, Shshank & Joshi, Dheeraj Kumar & Ujarari, Chandan Singh, 2023. "Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 98-107.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:98-107
    DOI: 10.1016/j.matcom.2022.09.019
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    References listed on IDEAS

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    1. Bin Zhu & Zeshui Xu & Meimei Xia, 2012. "Dual Hesitant Fuzzy Sets," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, May.
    2. Mohit Kumar & Shiv Prasad Yadav & Surendra Kumar, 2013. "Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 50-66.
    3. Akshay Kumar & S.B. Singh & Mangey Ram, 2020. "Systems reliability assessment using hesitant fuzzy set," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 38(1), pages 1-18.
    4. Ali Ebrahimnejad & Jose Luis Verdegay, 2018. "A new approach for solving fully intuitionistic fuzzy transportation problems," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 447-474, December.
    5. A.K. Shaw & T.K. Roy, 2013. "Trapezoidal intuitionistic fuzzy number with some arithmetic operations and its application on reliability evaluation," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 55-73.
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    1. Gupta, Soniya & Joshi, Dheeraj Kumar & Awasthi, Natasha & Pant, Manish & Joshi, Bhagawati prasad & Chaube, Shshank, 2024. "Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 321-336.

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