Generic Disjunctive Belief-Rule-Base Modeling, Inferencing, and Optimization

The combinatorial explosion problem is a great challenge for belief rule base (BRB) when a complex system has over-numbered attributes and/or referenced values for the attributes. This is because the BRB is conventionally constructed under the conjunctive assumption, conjunctive BRB, which requires covering each possible combination of all referenced values for all attributes. To solve this challenge, this study proposes a generic modeling, inferencing, and optimization approach for BRB under the disjunctive assumption, disjunctive BRB, that can significantly reduce its size. First, a disjunctive BRB is defined based on the mathematical description of the BRB space. The minimum size requirement for a disjunctive BRB is also discussed in comparison to a conjunctive one. Building on this, the generic disjunctive BRB modeling and inferencing procedures are proposed. Furthermore, an improved optimization model with further relaxed restrictions is constructed, and an optimization algorithm is developed in which only the new rule is optimized and its referenced values range is determined by the optimal solution in the former round optimization. The new optimization algorithm is more efficient with fewer variables and a more concise solution space. The results of three case studies confirm that by integrating both experts' knowledge and historic data, the modeling and inferencing processes can be well understood. Moreover, optimization can further improve the modeling accuracy while it facilitates downsizing the BRB in comparison with previous studies and other approaches.