An Exploration on Z-Number and Its Properties
Year: 2024
Type: article
Abstract: For better solving both fuzziness and reliability occurring in practical issues simultaneously, Z-number deserves further exploration under uncertainty environment. Based on the credibility distribution and conversion rules, we define its expected value, variance, and semi-variance, and realize the feasibility of calculation by deriving calculation formulas. Moreover, we delve into three characteristics inherent in symmetrical Z-numbers. The link that followed between the variance and the semi-variance of Z-numbers is discovered and proved. Furthermore, we apply the formulas of expected value and variance on Z-numbers to examples, whose consequences validate our proposed formulas. The findings indicate the significance of our study in applying the expected value and variance of fuzzy sets across diverse fields.
Source: Mathematics
DOI: 10.3390/math12193091
Authors: Guanshuang Jiang, Xinyu Shen, Xuefei Liao, Xiaoqi Xuan, Lechen Wu, Haomin Zhang, Zhen Li
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4403063415