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An Exploration on Z-Number and Its Properties

Author

Listed:
  • Guanshuang Jiang

    (School of Management, Shanghai University, Shanghai 200444, China)

  • Xinyu Shen

    (Qianweichang College, Shanghai University, Shanghai 200444, China)

  • Xuefei Liao

    (School of Economics and Management, Zhejiang Ocean University, Zhoushan 316022, China)

  • Xiaoqi Xuan

    (School of Management, Shanghai University, Shanghai 200444, China)

  • Lechen Wu

    (Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China)

  • Haomin Zhang

    (School of Management, Shanghai University, Shanghai 200444, China)

  • Zhen Li

    (School of Logistics and Maritime Studies, Bahrain Polytechnic, Isa Town 33349, Bahrain)

Abstract

The Z-number deserves further exploration in uncertain environments to effectively address fuzziness and reliability in practical issues simultaneously. Based on the credibility distribution and conversion rules, we define its expected value, variance, and semi-variance, and demonstrate the feasibility of these calculations by deriving formulas. Moreover, we explore three characteristics inherent in symmetrical Z-numbers. The link between the variance and semi-variance of Z-numbers is discovered and proved. Furthermore, we apply the formulas for expected value and variance to Z-numbers in examples, the results of which validate our proposed formulas. The findings underscore the significance of our study in applying the expected value and variance of fuzzy sets across diverse fields.

Suggested Citation

  • Guanshuang Jiang & Xinyu Shen & Xuefei Liao & Xiaoqi Xuan & Lechen Wu & Haomin Zhang & Zhen Li, 2024. "An Exploration on Z-Number and Its Properties," Mathematics, MDPI, vol. 12(19), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3091-:d:1491334
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    References listed on IDEAS

    as
    1. Jiskani, Izhar Mithal & Yasli, Fatma & Hosseini, Shahab & Rehman, Atta Ur & Uddin, Salah, 2022. "Improved Z-number based fuzzy fault tree approach to analyze health and safety risks in surface mines," Resources Policy, Elsevier, vol. 76(C).
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