An Exploration on Z-Number and Its Properties

Guanshuang Jiang, Xinyu Shen, Xuefei Liao, Xiaoqi Xuan, Lechen Wu, Haomin Zhang () and Zhen Li
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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

Mathematics, 2024, vol. 12, issue 19, 1-19

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.

Keywords: Z-numbers; expected value; variance; semi-variance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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