Indirect disjunctive belief rule base modeling using limited conjunctive rules: Two possible means

Abstract

A traditional Belief Rule Base (BRB) is constructed under the conjunctive assumption (conjunctive BRB), which requires covering the traversal combinations of the referenced values for the attributes. Consequentially, a traditional conjunctive BRB may have to face the combinatorial explosion problem when there are too many attributes and/or referenced values for the attributes. It is difficult or at least expensive to construct a complete conjunctive BRB, while it is easy to derive one or several conjunctive rules. Comparatively, a BRB under the disjunctive assumption (disjunctive BRB) requires only covering the referenced values for the attributes instead of the traversal combination of them. Thus, the combinatorial explosion problem can be avoided. However, it is difficult to directly obtain a disjunctive BRB from either historical data or experts' knowledge. To combine the advantages of both conjunctive and disjunctive BRBs, a new approach is proposed to construct a disjunctive BRB using a limited number of conjunctive rules (insufficient to construct a complete conjunctive BRB). In the new disjunctive BRB modeling approach, each disjunctive rule is derived by quantifying its correlation with one or multiple conjunctive rules. To do so, two means for belief generation are proposed, namely, equal probability and self-organizing mapping (SOM). Two cases are studied for validating the efficiency of the proposed approach. The results by the disjunctive BRB show consistency with those derived by the conjunctive BRB as well as other approaches, which validates the efficiency of the proposed approach considering that the disjunctive BRB is constructed with only a limited number of conjunctive rules.