TY - JOUR
T1 - Reformulation of Deng information dimension of complex networks based on a sigmoid asymptote
AU - Ortiz-Vilchis, Pilar
AU - Lei, Mingli
AU - Ramirez-Arellano, Aldo
N1 - Publisher Copyright:
© 2024 Elsevier Ltd
PY - 2024/3
Y1 - 2024/3
N2 - 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.
AB - 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.
KW - Asymptote
KW - Complex networks
KW - Deng's entropy
KW - Information dimension
KW - Mass function
UR - http://www.scopus.com/inward/record.url?scp=85184520790&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2024.114569
DO - 10.1016/j.chaos.2024.114569
M3 - Artículo
AN - SCOPUS:85184520790
SN - 0960-0779
VL - 180
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 114569
ER -