Basic probability assignment to probability distribution function based on the Shapley value approach

Multifractal analysis of mass function

In order to explore the fractal characteristic in Dempster-Shafer evidence theory, a fractal dimension of mass function is proposed recently, to reveal the invariance of scale of belief entropy. When mass function degenerates to probability, the fractal dimension is equivalent to classical Renyi information dimension only with α = 1 , which can measure the change rate of Shannon entropy with the size of framework. For Renyi dimension, different parameters α represent the relationship between different entropies and framework size. However, this compatibility is not shown in existing fractal dimension. Thus, in this paper, we introduce parameter α to generalize the existing dimension. Due to the diversity of the value of α , we name the new dimension: multifractal dimension of mass function. In addition, inspired by multifractal spectrum of Cantor set, we explore the relation between the belief degree of focal element and the number of focal element with same belief degree for some special assignments. Relevant results are also presented by spectrum. We provide a static discounting coefficient generating method to modify mass function to improve the accuracy of classify result. The experiment is conducted in three datasets, and the result shows the effectiveness of our method.

A Decision Probability Transformation Method Based on the Neural Network

When the Dempster-Shafer evidence theory is applied to the field of information fusion, how to reasonably transform the basic probability assignment (BPA) into probability to improve decision-making efficiency has been a key challenge. To address this challenge, this paper proposes an efficient probability transformation method based on neural network to achieve the transformation from the BPA to the probabilistic decision. First, a neural network is constructed based on the BPA of propositions in the mass function. Next, the average information content and the interval information content are used to quantify the information contained in each proposition subset and combined to construct the weighting function with parameter r. Then, the BPA of the input layer and the bias units are allocated to the proposition subset in each hidden layer according to the weight factors until the probability of each single-element proposition with the variable is output. Finally, the parameter r and the optimal transform results are obtained under the premise of maximizing the probabilistic information content. The proposed method satisfies the consistency of the upper and lower boundaries of each proposition. Extensive examples and a practical application show that, compared with the other methods, the proposed method not only has higher applicability, but also has lower uncertainty regarding the transformation result information.