Abstract: This paper constructs the basic probability assignment for the evidence theory applying in the problems of the ordered propositions. As a kind of typical classification problem, the ordered proposition is an active field in the applications of the evidence theory. Its basic probability assignment has distinct characteristics. By analyzing the features, the approach of typical sample is adopted. The Hamming distance between the practical value and typical value is used to obtain the density function of the normal distribution curve, which is applied to construct the basic probability assignment. The application is to evaluate the oil spill accident threaten degree, by which to analyze the shortcomings of this approach. The methods of increasing the Hamming distance flexibly and assigning the basic probability number nonzero for the ignorance are used to make the approach more feasible. The experiment results indicate that the approach proposed by this paper can assign the basic probability assignments effectively and satisfy the applications.

Key words: evidence theory, ordered proposition, basic probability assignment, typical sample

摘要： 针对证据理论在有序命题类问题中的应用构造基本概率分配函数。有序命题类问题作为一种常见的分类问题，是证据理论应用的一个活跃领域，其基本概率分配存在显著的特点，在分析其特征的基础上，采用基于典型样本的方法，利用实测值与典型值之间的距离构造正态分布曲线的密度函数，进而构造基本概率分配函数。将该方法应用于海上溢油事故等级的评定，通过数据模拟分析其存在的不足，并通过弹性拉大实测值与典型值之间的距离、将“不知道”概率赋值等方法进行改进。实验结果表明改进的基于典型样本的方法能够有效地进行基本概率分配，满足应用的特点和需要。

关键词: 证据理论, 有序命题, 基本概率分配, 典型样本