Abstract
Conflict evidence combination is an important research topic in evidence theory. In this paper, two kinds of transition matrices are constructed based on the Markov model; one is the unordered transition matrix, which satisfies the commutative law, and the other is the temporal transition matrix, which does not satisfy the commutative law, but it can handle the combination of temporal evidence well. Then, a temporal conflict evidence combination model is proposed based on these two transition matrices. First, the transition probability at the first n time is calculated through the model of unordered transition probability, and then, the transition matrix from the N + 1 time is used to solve the combination problem of temporal conflict evidence. The effectiveness of the transition matrix in the research of conflict evidence combination method is proved by the example analysis.
Highlights
Since the evidence theory was put forward by Dempster [1] in 1976, many experts and scholars have made in-depth research on the theory and applied it to the fields of uncertain reasoning, multisource information fusion, pattern recognition, and so on, and the evidence theory achieved good performance
The methods for resolving conflict evidence are mainly divided into two categories: one is to revise the evidence combination formula, which can be divided into three aspects: allocating conflict coefficients [2,3,4,5], changing combination rules [6], and expanding the recognition framework [7]
Jiang proposes a new correlation coefficient considering the nonintersection between focus elements and the difference between focus elements for the problems of unstable or insensitive quantization confidence of existing correlation coefficients in the aspect of allocating conflict coefficients; in the aspect of changing combination rules, the Murphy additive combination rule is proposed to solve the problem existed in the multiplicative rule of DS evidence theory; in the aspect of the expanding recognition framework, DSmT is developed, which changes the original recognition framework and extends it to the generalized power set. e other is to revise the original data, which can be divided into two aspects: one is to describe the uncertainty of evidence by distance, and the other is based on information entropy
Summary
Since the evidence theory was put forward by Dempster [1] in 1976, many experts and scholars have made in-depth research on the theory and applied it to the fields of uncertain reasoning, multisource information fusion, pattern recognition, and so on, and the evidence theory achieved good performance. E other is to revise the original data, which can be divided into two aspects: one is to describe the uncertainty of evidence by distance, and the other is based on information entropy. Rough the above literature, we find that the research on conflict evidence is almost based on uncertain information, which is the revision of conflict evidence at a certain time or under the general concept of time. In this case, all the source data are obtained at one time, and there is little research on whether the fusion order affects the fusion results. Park and Chang [31] and others used the DS theory to express and combine the estimated probabilities of three different statistical models and eliminated the probabilities of unknown states through the orthogonal sum of probabilities. e above literature shows that most of the fusion of temporal evidence is based on application. ere is no unified method to reflect the influence of time factors on the fusion of temporal evidence fully. erefore, this paper focuses on the characteristics of temporal evidence to build a unified temporal evidence fusion framework
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