The computational complexity of Dezert-Smarandache Theory (DSmT) increases exponentially with the linear increment of element number in the discernment frame, and it limits the wide applications and development of DSmT. In order to efficiently reduce the computational complexity and remain high accuracy, a new Evidence Clustering DSmT Approximate Reasoning Method for two sources of information is proposed based on convex function analysis. This new method consists of three steps. First, the belief masses of focal elements in each evidence are clustered by the Evidence Clustering method. Second, the un-normalized approximate fusion results are obtained using the DSmT approximate convex function formula, which is acquired based on the mathematical analysis of Proportional Conflict Redistribution 5 (PCR5) rule in DSmT. Finally, the normalization step is applied. The computational complexity of this new method increases linearly rather than exponentially with the linear growth of the elements. The simulations show that the approximate fusion results of the new method have higher Euclidean similarity to the exact fusion results of PCR5 based information fusion rule in DSmT framework (DSmT + PCR5), and it requires lower computational complexity as well than the existing approximate methods, especially for the case of large data and complex fusion problems with big number of focal elements.
Due to the huge computation complexity of Dezert-Smarandache Theory (DSmT), its applications especially for multi-source (more than two sources) complex fusion problems have been limited. To get high similar approximate reasoning results with Proportional Conflict Redistribution 6 (PCR6) rule in DSmT framework (DSmT + PCR6) and remain less computation complexity, an Evidence Clustering DSmT approximate reasoning method for more than two sources is proposed. Firstly, the focal elements of multi evidences are clustered to two sets by their mass assignments respectively. Secondly, the convex approximate fusion results are obtained by the new DSmT approximate formula for more than two sources. Thirdly, the final approximate fusion results by the method in this paper are obtained by the normalization step. Analysis of computation complexity show that the method in this paper cost much less computation complexity than DSmT + PCR6. The simulation experiments show that the method in this paper can get very similar approximate fusion results and need much less computing time than DSmT + PCR6, especially, when the numbers of sources and focal elements are large, the superiorities of the method are remarkable.
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