This research addresses two intensive computational problems of reasoning under uncertainty in artificial intelligence. The first problem is to study the strategy for belief propagation over networks. The second problem is to explore properties of operations which construe the behaviour of those factors in the networks. In the study of operations for computing belief combination over a network model, the computational characteristics of operations are modelled by a set of axioms which are in conformity with human inductive and deductive reasoning. According to different topological connection of networks, we investigate four types of operations. These operations successfully present desirable results in the face of dependent, less informative, and conflicting evidences. As the connections in networks are complex, there exists a number of possible ways for belief propagation. An efficient graph decomposition technique has been used which converts the complicated networks into simply connected ones. This strategy integrates the logic and probabilistic aspects inference, and by using the four types of operations for its computation it gains the advantage of better description of results (interval-valued representation) and less information needed. The performance of this proposed techniques can be seen in the example for assessing civil engineering structure damage and results are in tune with intuition of practicing civil engineers.
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