基于区间数的DS证据合成方法研究

Combination method for Dempster-Shafer theory of evidence based on interval numbers

在DS证据理论的应用过程中,命题的基本概率赋值函数起到了关键的作用,传统DS证据理论中基本概率赋值函数的取值为[0,1]中的单点值。在很难准确将证据所支持命题的基本概率赋值表示为[0,1]之间的单点值时,可以用区间数形式来表示命题的基本概率赋值。在建立符合运算封闭性的区间数广义求和与广义乘积算子的基础上,定义了基于区间数的基本概率赋值函数、信任函数以及似然函数等重要概念,给出了证据合成规则,进而提出了基于区间数的DS证据合成方法。计算实例表明,与传统DS证据合成方法相比,基于区间数的DS证据合成方法具有更灵活的应用特性和更小的计算复杂度。

With good performance in dealing with uncertain information, Dempster-Shafer theory of evidence （DST） is used in many practical aspects. And the basic probability assignment （BPA） plays a great role in its application. In the traditional DST, BPA is defined as a real number belonging to the range of [0, 1]. However, it is hard to provide such real numbers accurately in its practical applica- tions. The interval numbers were introduced into DST to solve this problem. Based on the establish- ment of the general addition and multiplication operators which satisfy the close of operation, the in- terval-valued BPA function, belief function and plausibility function were defined respectively, and the rule for combining pieces of evidence was presented in detail. Thus, the preliminary structure of DST based on interval numbers was discussed. Finally, an illustrative example proved that the novel method processes some advantages such as more flexibility and less computation complexity over the traditional one in DST.