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Article

An Exploration on Z-Number and Its Properties

1
School of Management, Shanghai University, Shanghai 200444, China
2
Qianweichang College, Shanghai University, Shanghai 200444, China
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School of Economics and Management, Zhejiang Ocean University, Zhoushan 316022, China
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Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
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School of Logistics and Maritime Studies, Bahrain Polytechnic, Isa Town 33349, Bahrain
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(19), 3091; https://doi.org/10.3390/math12193091
Submission received: 9 July 2024 / Revised: 20 September 2024 / Accepted: 1 October 2024 / Published: 2 October 2024

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 Z-numbers; expected value; variance; semi-variance

Share and Cite

MDPI and ACS Style

Jiang, G.; Shen, X.; Liao, X.; Xuan, X.; Wu, L.; Zhang, H.; Li, Z. An Exploration on Z-Number and Its Properties. Mathematics 2024, 12, 3091. https://doi.org/10.3390/math12193091

AMA Style

Jiang G, Shen X, Liao X, Xuan X, Wu L, Zhang H, Li Z. An Exploration on Z-Number and Its Properties. Mathematics. 2024; 12(19):3091. https://doi.org/10.3390/math12193091

Chicago/Turabian Style

Jiang, Guanshuang, Xinyu Shen, Xuefei Liao, Xiaoqi Xuan, Lechen Wu, Haomin Zhang, and Zhen Li. 2024. "An Exploration on Z-Number and Its Properties" Mathematics 12, no. 19: 3091. https://doi.org/10.3390/math12193091

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