An evidence clustering DSmT approximate reasoning method based on convex functions analysis

Abstract

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.

Fault Diagnosis Method for a Mine Hoist in the Internet of Things Environment

“…The combination characteristic of DSmT can solve this problem effectively. The conflict rules are omitted, and the loss of effective information can be avoided [ 34 , 35 ].…”

An evidence clustering DSmT approximate reasoning method for more than two sources

“…, the convex function error analysis can be seen in [44] and the convex error function formula is given by…”

“…With the rapid development of science and technology, sensor types become diverse. To solve the more and more complex practical problems, information fusion from different multi sources has been drawn great attention by scholars in recent years [1][2][3][4][5][6][7][8][9][10][11][12]. Due to the influence of noise, uncertain signal and information processing has become an important research direction in the field of information fusion.…”

“…Applied mathematics has drawn attention by many scholars [39,40]. Particularly, the very recent Evidence Clustering DSmT Approximate Reasoning Method based on Convex Function Analysis [11] proposed by Guo, He, et al can get very similar approximate fusion results with PCR5 in DSmT framework and cost little computation complexity. Nevertheless, the approximate method in [11] is only for two sources and it is not associative in the fusion of multiple (more than 2) sources of evidences.…”