A distance-based approach for merging probabilistic knowledge bases

In the stages of development of probabilistic expert systems, knowledge merging is a major concern. To deal with knowledge merging problems, several approaches have been put forward. However, in the proposed models, each original probabilistic knowledge base (PKB) is represented by a set of probabilistic functions fulfilling such knowledge base. The drawbacks of the solutions are that the output of model is also a set of probabilistic functions satisfying the resulting PKB and there is no algorithm for implementing the merging process of PKBs in which each of them consists of probabilistic constraints. In this paper, distance-based approach is utilized to propose a new method of merging PKBs to ensure that both the input and output of methods are represented by sets of probabilistic constraints. To this aim, the relationship between the probability rules and the probabilistic constraints, and the several transformation methods for the representation of the original PKB are presented, a set of merging operators (MOs) is proposed, and several desirable logical properties are investigated and discussed. Several algorithms for merging PKBs are presented and the computational complexities of these algorithms are also analyzed and evaluated.