基于广义三角模糊数的基本概率赋值构造方法

Basic probability assignment construction method based on generalized triangular fuzzy number

Dempster组合规则的有效运用取决于相应基本概率赋值的合理建立,但是如何生成各个证据的基本概率赋值仍然是一个有待解决的问题。基于广义三角模糊数表示模型,提出了一种基本概率赋值生成方法。该方法利用样本数据的最小值、平均值和最大值构造单元素命题的三角模糊数表示模型,多子集命题的广义三角模糊数用单元素命题的三角形的交叠部分来表示。通过广义三角模糊数的隶属度来构造基本概率赋值。数值算例结果表明,提出的基本概率赋值获取方法是实用有效的。

The effective application of Dempster＇ s combination rule depends on the rational construction of corre- sponding basic probability assignment （BPA）. However, how to determine basic probability assignment is still an open issue. Based on the generalized triangular fuzzy number model, a method for obtaining basic probability assignment is proposed. In this proposed method, the triangular fuzzy number model of singleton proposition is constructed using the minimum, average and maximum values of the sample data. The generalized triangular fuzzy number model of multiele- ment proposition is represented by the crossing area of the fuzzy numbers of the singleton propositions. Based on the degree of membership of the generalized triangular fuzzy number, the basic probability assignments are obtained. Nu- merical examples indicate that the proposed method for determining basic probability assignment is practicable.