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Deng entropy is a novel and efficient uncertainty measure to deal with imprecise phenomenon, which is an extension of Shannon entropy. In this paper, power law and dimension of the maximum value for belief distribution with the max Deng entropy are presented, which partially uncover the inherent physical meanings of Deng entropy from the perspective of statistics. This indicated some work related to power law or scale-free can be analyzed using Deng entropy. The results of some numerical simulations are used to support the new views. INDEX TERMS Deng entropy, power law, maximum Deng entropy, dimension.

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Collapse is the main engineering disaster in tunnel construction when using the drilling and blasting method, and risk assessment is one of the important means to significantly reduce engineering disasters. Aiming at the problems of random decision-making and misjudgment of single indices in traditional risk assessment, a multi-source data fusion method with high accuracy based on improved Dempster–Shafer evidence theory (D-S model) is proposed in this study, which can realize the accurate assessment of tunnel collapse risk value. The evidence conflict coefficient K is used as the identification index, and the credibility and importance are introduced. The weight coefficient is determined according to whether the conflicting evidence is divided into two situations. The advanced geological forecast data, on-site inspection data and instrument monitoring data are trained by Cloud Model (CM), Gradient Boosting Decision Tree (GBDT) and Support Vector Classification (SVC), respectively, to obtain the initial BPA value. Combined with the weight coefficient, the identified conflict evidence is adjusted, and then the evidence from different sources is fused to obtain the overall collapse risk value. Finally, the accuracy is selected to verify the proposed method. The proposed method has been successfully applied to Wenbishan Tunnel. The results show that the evaluation accuracy of the proposed multi-source information fusion method can reach 88%, which is 16% higher than that of the traditional D-S model and more than 20% higher than that of the single-source information method. The high-precision multi-source data fusion method proposed in this paper has good universality and effectiveness in tunnel collapse risk assessment.