1. Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote.
- Author
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Ortiz-Vilchis, Pilar, Lei, Mingli, and Ramirez-Arellano, Aldo
- Subjects
- *
FRACTAL dimensions , *ASYMPTOTES , *LOGARITHMIC functions , *INFORMATION networks - Abstract
Deng's entropy is a measure used to determine the volume fractal dimension of a mass function. It has been employed in pattern recognition and conflict management applications. Recently, Deng's entropy has been employed in complex networks to measure the information volume when handling complex and uncertain information. The general asymptote for computing the Deng information dimension of complex networks was assumed to be a power law in a previous study; meanwhile, the asymptote to obtain the information dimension is a logarithmic function. This study proposes a sigmoid asymptote for Deng's information dimensions in complex networks. This new formulation shows that the non-specificity is maximal at ɛ = 1 and minimal when ɛ = Δ. The oppositive occurs with the maximum discord at ɛ = 1 and minimal discord at ɛ = Δ. In addition, the asymptotic values η and δ and the inflexion point ψ of the Deng entropy of the complex networks were revealed. Twenty-eight real-world and 789 synthetic networks were used to validate the proposed method. Our results show that the sigmoid asymptote best fits the empirical Deng entropy and d s D differs substantially from d D and d d D. In addition, d s D more accurately characterises the synthetic networks. • A sigmoid asymptote is proposed for Deng's information dimension. • The asymptotic values of η , δ and the inflexion point of ψ for the Deng entropy of complex networks are provided. • This new formulation shows that the non-specificity is at its maximum when ɛ = 1 and at its minimum when ɛ = δ. • The latest formulation demonstrates the maximum discord at ɛ = 1 and the minimum at ɛ = δ. • Rather than a power law or logarithmic function, the suggested asymptote more accurately describes Deng's entropy. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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