D-S证据理论中的基本概率赋值转换概率方法研究

A Probabilistic Transformation of Basic Probability Assignment (BPA) in D-S Evidence Theory

D-S证据理论的基本概率赋值(BPA)能够有效地表示和处理不确定信息,在不确定信息处理中得到了越来越多的应用。但是如何基于BPA做出决策依然是一个有待解决的问题,将BPA转化为概率函数进行决策是一个简单可行的方法。文章基于证据理论中命题的信度函数和似真函数提供的信息,提出了一种新的基本概率赋值转换概率方法,该方法相比于现有经典TBM模型中Pignistic概率转换和基于似真函数的转换,可以更有效地利用系统已知的信息,实现基本概率赋值到概率分布的合理转换。算例表明了所提出方法的有效性。

The BPA in the Dempster-Shafer（D-S） evidence theory can effectively represent and process the uncertainty information and it has been widely used in various fields. But the problem of how to make decisions based on BPA still needs to be solved. To transform BPA into probability function is a simple and feasible solution, so we propose what we believe to be a new method for transforming BPA into probability by utilizing the information contained in the belief function and plausibility function of the propositions in the D-S evidence theory. Compared with the existing Pignistie Probability Transform based on the transferable belief model and the plausibility function transform, our probability transformation method can more effectively utilize the known information of a target identification system and achieve the reasonable transformation from BPA to probability distribution. A numerical example also verifies that our method can measure the effects of the belief function and the plausibility function on the distribu- tion of BPA to the multi-subset propositions. All these indicate that our method is effective.