基本概率赋值不确定性的广义度量及在证据组合中的应用

A generalized measure of basic probability assignment uncertainty and its application in evidence combination

中文关键词  D–S证据理论  改进的归一化投影  不确定性广义度量  证据组合

英文关键词  D–S evidence theory  improved normalized projection  generalized measure of uncertainty  evidence combination

中文摘要

      D–S证据理论中一个关键问题是度量传感器给出的基本概率赋值(BPA)的不确定性大小, 它的准确度量对 于评估信任结构传递的信息量至关重要. 本文首先提出了改进的归一化投影方法(iNP), 然后基于iNP提出了一种新 的投影不确定性(PU)广义度量方法, 理论证明和实验仿真说明了PU满足非负性、有界性、不变性、单调性、不反直 观性、较高的敏感性和较低的计算负担等性质, 这些性质保证了PU可以有效对BPA的不确定性广义度量. 与现有的 不确定性度量方法相比, 所提出的方法对证据的变化更为敏感. 最后, 基于PU方法给出了一种新的证据组合方法, 通过数值实例和实际应用, 说明了本文所提方法的有效性和合理性.

英文摘要

      Measurement of the uncertainty of the basic probability assignment (BPA) given by the sensor is a key issue in the D–S (dempster-shafer) evidence theory, and the accuracy level of the uncertainty is crucially important to assess the quality of information conveyed by belief structures. This paper first proposes an improved normalized projection method (iNP), and then presents a new generalized measure of projection uncertainty (PU) based on iNP. Theoretical proofs and experimental simulations illustrate that PU satisfies the properties of nonnegativity, boundness, invariance, monotonicity, non-reverse intuition, higher sensitivity and lower computational burden, which ensure that PU can effectively realize generalized measure of BPA uncertainty. Compared with the existing uncertainty measures, the proposed method is more sensitive to changes in evidence. Finally, a new evidence combination method based on the PU method is put forward, and the effectiveness and the rationality of the proposed method are illustrated by numerical examples and practical applications.