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For a certain moment, the information volume represented in a probability space can be accurately measured by Shannon entropy. But in real life, the results of things usually change over time, and the prediction of the information volume contained in the future is still an open question. Deng entropy proposed by Deng in recent years is widely applied on measuring the uncertainty, but its physical explanation is controversial. In this paper, we give Deng entropy a new explanation based on the fractal idea, and proposed its generalization called time fractal-based (TFB) entropy. The TFB entropy is recognized as predicting the uncertainty over a period of time by splitting times, and its maximum value, called higher order information volume of mass function (HOIVMF), can express more uncertain information than all of existing methods.
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm of a posit
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two pictures. We give
Given a probability measure $mu$ over ${mathbb R}^n$, it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan used a stoch
The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter $p$ (BSMS($p$)) with Hammi
A finite form of de Finettis representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $ngeq k$ is close to a mixture of product d