An approximate reasoning method in Dezert-Smarandache Theory

Abstract

With the increment of focal elements number in discernment framework, the computation amount in Dezert-Smarandache Theory (DSmT) will exponentially go up. This has been the bottleneck problem to block the wide application and development of DSmT. Aiming at this difficulty, in this paper, a kind of fast approximate reasoning method in hierarchical DSmT is proposed. Presently, this method is only fit for the case that there are only singletons with assignment in hyper-power set. These singletons in hyper-power set are forced to group through bintree or tri-tree technologies. At the same time, the assignments of singletons in those different groups corresponding to each source are added up respectively, in order to realize the mapping from the refined hyper-power set to the coarsened one. And then, two sources with the coarsened hyper-power set are combined together according to classical DSm Combination rule (DSmC) and Proportional Conflict Redistribution rule No. 5 (PCR5). The fused results in coarsened framework will be saved as the connecting weights between father and children nodes. And then, all assignments of singletons in different groups will be normalized respectively. Tree depth is set, in order to decide the iterative times in hierarchical system. Finally, by comparing new method with old one from different views, the superiority of new one over old one is testified well.