Journal: Fractals

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World Scientific

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2018 - 201922020 - 20223
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Publications 1 - 5 of 5
  • Cutting self-similar space-filling sphere packings
    Item type: Journal Article
    Stäger, D.V.; Herrmann, Hans Jürgen (2018)
    Fractals
  • Information fractal dimension of mass function
    Item type: Journal Article
    Qiang, Chenhui; Deng, Yong; Cheong, Kang Hao (2022)
    Fractals
    Fractals play an important role in nonlinear science. The most important parameter when modeling a fractal is the fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, calculating the fractal dimension given a mass function, which is the generalization of probability, is still an open problem of immense interest. The main contribution of this work is to propose an information fractal dimension of mass function. Numerical examples are given to show the effectiveness of our proposed dimension. We discover an important property in that the dimension of mass function with the maximum Deng entropy is ln 3 ln 2 ≈ 1.585, which is the well-known fractal dimension of Sierpiski triangle. The application in complexity analysis of time series illustrates the effectiveness of our method.
  • Self-Similar Space-Filling Sphere Packings in three and four Dimensions
    Item type: Journal Article
    Stäger, Dominik V.; Hermann, Hans J. (2018)
    Fractals
  • Information Dimension of Galton Board
    Item type: Journal Article
    Zhou, Qianli; Deng, Yong; Pedrycz, Witold (2022)
    Fractals
    In this paper, we relax the definition of Renyi information dimension. The power law of the Entropy-Layer in the Galton board is discovered and we calculate its information fractal dimension. When the Galton board is extended to bias or three-dimensional space, we get the same fractal features. In addition, according to the connection between Pascal's triangle and the Poisson distribution, we find constrained Poisson distribution groups with the same information dimension. This is the first time the information entropy is utilized to explore the fractal features of the Galton board and Pascal's triangle.
  • Information Volume Fractal Dimension
    Item type: Journal Article
    Gao, Qiuya; Wen, Tao; Deng, Yong (2021)
    Fractals
    There has been immense interest in uncertainty measurement because most real-world problems are accompanied by uncertain events. Therefore, Deng entropy has been proposed to measure the uncertainty in the probability theory and evidence theory. In this paper, we show that the uncertainty of the basic probability assignment (BPA) separated through the maximum Deng entropy separation rule (MDESR) is larger than the maximum Deng entropy of the original BPA. In addition, when the cardinality of the frame of discernment increases, the maximum information volume becomes larger and converges slower. The information volume fractal dimension is then proposed to describe the fractal property of uncertainty about the separated BPA distribution, which indicates the inherent physical meanings of Deng entropy from the perspective of statistics. This work can inspire further research on the fractal property of Deng entropy. Some experiments are applied to show the applicability of our proposed information volume fractal dimension.
Publications 1 - 5 of 5