Yang Yi, Liu Yuanli
SKLSVMS, School of Aerospace, Xi'an Jiaotong University, Xi'an, Shaanxi, China 710049.
PLoS One. 2016 Feb 1;11(2):e0147799. doi: 10.1371/journal.pone.0147799. eCollection 2016.
In the theory of belief functions, the approximation of a basic belief assignment (BBA) is for reducing the high computational cost especially when large number of focal elements are available. In traditional BBA approximation approaches, a focal element's own characteristics such as the mass assignment and the cardinality, are usually used separately or jointly as criteria for the removal of focal elements. Besides the computational cost, the distance between the original BBA and the approximated one is also concerned, which represents the loss of information in BBA approximation. In this paper, an iterative approximation approach is proposed based on maximizing the closeness, i.e., minimizing the distance between the approximated BBA in current iteration and the BBA obtained in the previous iteration, where one focal element is removed in each iteration. The iteration stops when the desired number of focal elements is reached. The performance evaluation approaches for BBA approximations are also discussed and used to compare and evaluate traditional BBA approximations and the newly proposed one in this paper, which include traditional time-based way, closeness-based way and new proposed ones. Experimental results and related analyses are provided to show the rationality and efficiency of our proposed new BBA approximation.
在信度函数理论中，基本信度分配（BBA）的近似是为了降低高计算成本，尤其是在有大量聚焦元素的情况下。在传统的BBA近似方法中，聚焦元素自身的特征，如质量分配和基数，通常单独或联合用作去除聚焦元素的标准。除了计算成本外，原始BBA与近似BBA之间的距离也受到关注，它表示BBA近似中的信息损失。本文提出了一种基于最大化接近度的迭代近似方法，即最小化当前迭代中的近似BBA与上一次迭代中获得的BBA之间的距离，其中每次迭代去除一个聚焦元素。当达到所需的聚焦元素数量时，迭代停止。还讨论了BBA近似的性能评估方法，并用于比较和评估传统的BBA近似和本文新提出的方法，包括传统的基于时间的方法、基于接近度的方法和新提出的方法。提供了实验结果和相关分析，以展示我们提出的新BBA近似的合理性和效率。
