Structure learning for belief rule base expert system: A comparative study

The Belief Rule Base (BRB) is an expert system which can handle both qualitative and quantitative information. One of the applications of the BRB is the Rule-base Inference Methodology using the Evidential Reasoning approach (RIMER). Using the BRB, RIMER can handle different types of information under uncertainty. However, there is a combinatorial explosion problem when there are too many attributes and/or too many alternatives for each attribute in the BRB. Most current approaches are designed to reduce the number of the alternatives for each attribute, where the rules are derived from physical systems and redundant in numbers. However, these approaches are not applicable when the rules are given by experts and the BRB should not be oversized. A structure learning approach is proposed using Grey Target (GT), Multidimensional Scaling (MDS), Isomap and Principle Component Analysis (PCA) respectively, named as GT–RIMER, MDS–RIMER, Isomap–RIMER and PCA–RIMER. A case is studied to evaluate the overall capability of an Armored System of Systems. The efficiency of the proposed approach is validated by the case study results: the BRB is downsized using any of the four techniques, and PCA–RIMER has shown excellent performance. Furthermore, the robustness of PCA–RIMER is further verified under different conditions with varied number of attributes.