Variance of belief information

In alignment with the law of large numbers, the Gaussian distribution is a prevalent occurrence characterized by its expectation and variance. The expectation denotes the mean state of the system, whereas the variance encapsulates the system's degree of fluctuation. Information entropy represents the expectation of information content, with Deng entropy extending this concept to the distribution of mass. As a pivotal attribute of complex systems, the variance of the associated information remains an unresolved issue. This paper introduces the concept of belief information variance, addressing a void within the mass function framework. It delves into the mathematical attributes of this proposed variance, including non-negativity, translation invariance, and homogeneity. Utilizing the principle of entropy increase, the paper investigates the temporal dynamics of variance by traversing the mass space, uncovering two types of dynamic orbits on complex surfaces. Moreover, classification experiments on real-world datasets demonstrate that incorporating the variance improves classification accuracy of evidential decision making methods. The introduction of the variance offers a theoretical foundation for exploring the volatility of belief information.