Logical method for logical operations based on evidential reasoning

Abstract

The purpose of this paper is to employ Dempster-Shafer theory in problems which are defined in hierarchical and logical structures such as a fault tree. One of main differences of the Dempster-Shafer theory from Bayesian one is that the Dempster-Shafer method enables us to take the lack of knowledge or information into consideration in its analyses. A focal set of hypotheses must be mutual exclusive and exhaustive in the Dempster-Shafer theory. In this paper, we define state patterns in order to satisfy the mutual exclusiveness and exhaustiveness. The method using state patterns requires us much computational time due to the huge number of combinatorials to solve the evidential reasoning. In order to resolve this issue, this paper provides the improved method based on logical relations in the hierarchical structure.