Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote

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 dsD differs substantially from dD and ddD. In addition, dsD more accurately characterises the synthetic networks.