The Research Of Combination Algorithms Of Weighted Evidence

The application of expert systems is all along the research focus in Artificial Intelligence. Many expert systems have been proved very effective in the application domains such as agriculture, medical, geology, etc. However, in many application domains, there is usually much more imprecise or uncertain knowledge rather than precise information to support the decision. Therefore, uncertain, or imprecise, reasoning model is required to deal with the uncertain evidence and knowledge. Dempster-Shafer theory, also called evidence theory or D-S theory, is a kind of model-based approach in uncertain reasoning which provides a way to represent knowledge of domain and a reasoning machinism based on that knowledge representation. Along with the improvement of the performance of the computer systems and the research progress of algorithms in D-S theory, the theory has already been applied in many applications and been one of the most effective approaches to solve uncertain problems. In the respresention of uncertain knowledge with D-S theory, the evidence is usually organized into a network, of which there is a typical kind called Dempster-Shafer network or D-S network. D-S network and another well-known structure, Bayesian network, are all the instances of belief networks. In D-S network, belief propagation is carried out by the combination of evidence. Unlike the rule-based reasoning, D-S network doesn't designate explicit reasoning directions. This makes it possible to acquire abitrary unknown beliefs in the network, given some already known beliefs, by belief propogation. Such knowledge organizing machinism brings about much more flexibility to knowledge representation and reasoning. Pragmatically, D-S theory has some drawbacks, one of which is that Dempster rule can produce paradoxical results which are inconsisitent with the human's intuitive impression. The problem has been studied, and many combining rules to solve the conflict have been proposed, such as disjunctive rule, Smets rule, Yager rule, Dubois-Prade rule, general weighted operator, weighted average operator, minC rule, PCR rule, etc. Among these rules, some are mutable and associative such as disjunctive rule, Smets rule and minC rule. Since, in the real world, the reliabilities of the evidence sources differ from one another, it will be very necessary to account for the reliabilities in the combination. However, the existing combining rules of conflicting evidence almost all ignored the information of reliabilities. So, it is of promising significance to study the algorithms for combining evidence with different reliabilities. First, we introduced the concept of weighted belief function which models the reliability in the real world by mapping it to the weight of evidence, a real number within [0, 1]. Concerned with reliabilities, we made some experiments on the existing combining rules and did not obtain any satisfactory results. Therefore, we proposed three combining rules of weighted belief functions which were WPCR rule, WminC rule and Alpha rule based on the consistence preprocessing representively. WPCR rule is based on the proportional redistribution of conflict. The evidence sources are first combined by conjunctive consensus and the weights information (weight matrix SUM_W in WPCR) and the statistical information of evidence sources (maximum belief function value MAX_M, minimum belief function value MIN_M, average belief function value ARG_M) are recorded. Then the whole conflict is distributed proportionally according to the recorded information. WminC rule is similar to WPCR rule in that it is also based on the proportional redistribution of conflict with the aid of recorded statistical information. While, different from WPCR, general conjunctive consensus proposed in minC rule is adopted in the first step of WminC instead of conventional conjunctive consensus and the partial conflict is then proportionally redistributed instead of the whole confliction. Alpha rule differs from WPCR and WminC in the theory foundation which is based on the preprocessing of source evidence and leverages the Dempster rule to get the finial result. In Alpha rule, the preprocessing is called consistent processing, which does not necessarily preprocess all the focal elements. Three criteria were given for the selection of the focal elements to be preprocessed which ensure the selected focal elements to be just concerned with conflict. Besides, the determination of the disturbance factor essentially needed in the Alpha rule is built on the optimal estimation of combination effect, so the results of combination are satisfactory. Some relative mathematical analysis on Alpha rule was given in the paper. Due to the fact that each time only two pieces of evidence are combined and the combined result may be combined straightly with other evidence, the combination of weight is included in the overall combination procedure, so that the capsulation of the rule is garanteed. Since, in WPCR and WminC, distribution of conflict is performed right after the conjunctive consensus, WPCR and WminC keep the mutability and...