# TMVDPatch: A Trusted Multi-View Decision System for Security Patch Identification
## 2 Background and Related Work
### Uncertainty and the Theory of Evidence  
At present, in the work of realizing security patch identification based on neural network, the softmax output is often used as the classification result. However, this method leads to high over-confidence even for false identification [28; 29]. Dempster Shafer theory provides a solution to this problem, as a theory on belief functions, which allows beliefs from different sources to be combined with various fusion operators to obtain a new belief that considers all available evidence. In addition, [PERSON] [30] proposes a fuzzy soft set approach in decision making based on Grey Relational Analysis and Dempster-Shafer theory of evidence. They use the Grey Relational Analysis to determine the uncertain degrees of various parameters. Moreover, subjective logic proposes a solution to the quantification and consolidation of multi-view.  
Grey Relational Analysis [31; 32; 33] is an approach for multi-criteria decision making that measures the similarity or dissimilarity between variables of a process. It can help assess the impact of different factors on the outcome. Evidence theory is a mathematical framework for handling uncertain information. It can be used to fuse data from multiple views. Based on the above analysis, this paper believes that the advantages of combining Grey Relational Analysis and evidence theory for multi-view learning can be summarized as follows:  
* Grey Relational Analysis can preprocess multi-view data, reducing data dimensionality and noise.
* Evidence theory can dynamically integrate multi-view data, considering the uncertainty and weight of each view.  
* The performance and robustness of multi-view classification can be enhanced, as well as the confidence and interpretability of the decision.  
Therefore, based on subjective logic, this paper obtains identification evidence from the multi-view, and combines the Dirichlet distribution to obtain the belief quality and uncertainty quality of security patch identification, and then solves the problem of softmax over-confidence. At the same time, this paper uses the Dirichlet distribution to give the neural network classification results a probability distribution density, and then realizes the second-order probability and uncertainty of the simulated output. Unlike [30], we determine the relationship of different views as the weight of evidence input according to the Grey Relational Analysis method, and make self-learning correction. The specific details are discussed in detail in the Section 4.5.  
Subjective Logic [34; 35; 36; 37; 38] provides a theoretical framework for the relationship between Dirichlet distribution parameters and belief and uncertainty. The framework formalizes the concept of belief distribution of DST (Dempster-Shafer Theory of Evidence) [39] as Dirichlet distribution [40; 41] in the identification framework. Specifically, subjective logic provides a framework that provides each category with a belief quality \(b_{k}\) and an overall uncertainty quality \(u\). Intuitively, the belief quality \(b_{k}\) is the probability of different categories based on the collected evidence, and the uncertainty quality \(u\) is the overall uncertainty of the probability of a specific category, where \(k=1,2,\cdots,K\) represents the category in the \(K\) classification. Moreover, the belief quality and uncertainty quality are both positive numbers, and the sum is 1. The formula is satisfied [42]:  
\[u+\sum_{k=1}^{K}b_{k}=1 \tag{1}\]