Logical computation of evidential reasoning in a hierarchical structure

Our objective is to employ Dempster-Shafer theory into analyzing the hierarchical and logical structure with logical operations AND & OR such as a fault tree. One of main differences of the Dempster-Shafer theory from Baysian one is that it enables us to take the lack of knowledge or information into account in its analyses. The considered set of hypothesis must be mutual exclusive and exhaustive in the Dempster-Shafer theory. We define state patterns in order to satisfy the mutual exclusiveness and exhaustiveness. The method using state patterns requires us much computational time to solve the evidential reasoning. In order to overcome this difficulty, we also propose the improved method in terms of logical relations of the events in the fault tree.