The Theory And Application Of The Transferable Belief Model

Content: In this paper, there are two parts research on the transferable belief model(TBM).One is theoretic research on the TBM. Firstly, the TBM is compared with the classical probability model, the upper and lower probabilities model, and Dempster's model. By successively analyzing the static component and the dynamic component of these models, we can find out the essential difference between the TBM and the above probability models: indeed there are no necessary links between the TBM and any theory of probability. Secondly, we define a pair of Rough operators on the TBM and give some of the properties of them. We then use the pair of Rough operators to interpret belief functions and plausibility functions on the TBM.The other is applied research on the TBM: this is the very emphasis of this paper.For processing training patterns with imprecise class labels, this paper presents the k-nearest neighbor classification rule based on the TBM and its generalization combined with fuzzy sets and possibility theory. It's convenient to make decision about the true class membership of a pattern to be classified by the application of the pignistic transformation. In the finite frame of discernment, the normalized fuzzy set can generate a possibility measure through the associated membership function, and the possibility measure is a plausibility measure. So it is feasible to generalize the k-NN rule based on the TBM.In addition, an adaptive method to tune automatically the parameters in the two presented classification rules is proposed. The method is based on minimizing an error function between the output class labels and target class labels of the training patterns by gradient descent.Finally, the computer simulations are performed experimentally to compare the above rules. The simulated results show that the generalized rule outperform obviously the k-NN rule based on the TBM, and the two presented rules make a better improvement after the parameter optimization.