Knowledge fusion using Dempster-Shafer theory and the imprecise Dirichlet model

In many data mining applications, a large number of expert statements have to be fused, for example statements concerning class labels of data samples. Often, the experts do not agree, that is, they hold conflicting beliefs. There exist various combination rules that could be used to fuse such expert knowledge. We claim that, in addition to existing requirements in combination rules, the numerical evaluation of fused beliefs must reflect any persistent conflicts. We investigate three combination rules, the original Dempster-Shafer rule, Murphy´s rule, and a rule based on the imprecise Dirichlet model, and show theoretically and empirically that the former two have a convergence behavior which does not comply with the new requirement. Only the rule based on the imprecise Dirichlet model exhibits the required behavior when a large number of statements is fused. We also discuss how a rule based on the imprecise Dirichlet model may be used in the fields of collaborative knowledge discovery & data mining or organic computing.