An Exploration on Z-Number and Its Properties

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.