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Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

Author

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  • Mohit Kumar
  • Shiv Prasad Yadav
  • Surendra Kumar

Abstract

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:1:p:50-66
    DOI: 10.1080/00207721.2011.581393
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    Cited by:

    1. 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.
    2. Aayushi Chachra & Mangey Ram & Akshay Kumar, 2024. "Fuzzy reliability framework under hesitant and dual hesitant fuzzy sets to air conditioning system," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 603-627, June.
    3. Junhua Hu & Xiaolong Zhang & Xiaohong Chen & Yongmei Liu, 2016. "Hesitant fuzzy information measures and their applications in multi-criteria decision making," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(1), pages 62-76, January.
    4. Chachra, Aayushi & Kumar, Akshay & Ram, Mangey, 2023. "Intuitionistic fuzzy approach to reliability assessment of multi-state systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 489-503.

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