直觉模糊框架内的区间证据组合方法研究

区间证据的组合是区间证据理论中的核心问题之一,尽管相关学者试图将D-S证据理论中的证据组合规则进行推广以实现区间证据的组合,但该问题仍未得到完全解决.目前已有的组合方法都是基于优化模型来确定融合结果中各基本概率质量(BPM)的上下界,不仅算法复杂度较高,而且这类方法不满足结合律,对多个区间证据进行组合时不能依次对各个证据进行组合,难以满足时域信息融合的需求.本文基于直觉模糊集与证据理论之间的关系,在直觉模糊框架内对区间证据的组合问题进行研究.首先基于证据理论定义一种新的直觉模糊运算,通过区间证据与直觉模糊集之间的相互转换,提出一种基于直觉模糊集的区间证据组合方法,该方法满足交换律和结合律,对多个区间证据进行组合时具有较强的灵活性.数值仿真表明,基于直觉模糊集的区间证据组合方法可以获得合理的组合结果,而且算法复杂度远低于现有方法.

Combining interval-valued belief functions in the framework of intuitionistic fuzzy sets

Theory of belief function can be introduced to the interval set by defining interval-valued belief functions. The Dempster-Shafer (D-S) evidence theory has been extended to combine interval-valued belief functions for decades. Although there already exist several combination approaches proposed by previous researchers, this problem has not been fully resolved so far. A novel combination of interval-valued belief functions is developed after analyzing existing irrational or suboptimal approaches. The novel combination approach is modeled based on intuitionistic fuzzy set, rather than nonlinear programming models, which are computational complicated. Numerical examples are implemented to illustrate the performance of the proposed approach.