# Cross-Domain Fake News Detection Through Fusion of Evidence from Multiple Social Media Platforms
## 3 System Architecture
\begin{cases}0,&\text{when }U\approx 1\\ \min\left(\left\{p_{i\_r\_d}^{c}\right\}_{i\_r\_d}^{n},1-U\right),&\text{ otherwise}\end{cases}  \tag{4}\]  
So, after completing this step, we obtain a'support' probability and a 'non-support' probability for each comment on both social media platforms. Given that we have \(n\) comments from both Twitter and Reddit, after this step we have \(n\) support and \(n\) non-support probabilities for each platform. Additionally, a common uncertainty, \(U\), value is associated with every comment across all platforms. * Fuse the support probabilities: afterwards, the pairwise support probabilities of comments from both Twitter and Reddit are fused using the Dempster-Shafer (DS) combination rule. This approach involves combining the support probabilities from both platforms according to the equation below. The combined support probability for the \(i\)-th comment using Dempster-Shafer theory [66] is: \[m_{i}=\frac{p_{i\_r\_to}^{\sup}\cdot p_{i\_r\_d}^{\sup}+p_{i\_r\_ \text{ind}}^{\sup}\cdot U+U\cdot p_{i\_r\_d}^{\sup}}{1-(p_{i\_tw}^{\sup}\cdot p _{i\_r\_d}^{-\sup}+p_{i\_tw}^{-\sup}\cdot p_{i\_r\_d}^{\sup})}\] (5) Since there are a total of \(n\) comments, the combined values form a list, \(m_{i}\), for \(i=1,2,\ldots,n\). * Aggregate the fused decision: after fusing the decisions from comments on two different platforms using Dempster-Shafer theory, we aggregate the combined support probabilities, \(m_{i}\), to obtain the final probability, \(p_{\text{final}}\). This is done by first determining the majority class of the support values (whether more values are equal or greater than 0.5 or less than 0.5) and then averaging the support values that belong to the majority class. This approach ensures a comprehensive and balanced assessment of the information gathered from both Twitter and Reddit comments. \[P_{\text{final}}=\frac{1}{g}\sum_{i\in\text{majority}}m_{i}\] (6) where \(g\) is the number of \(m_{i}\) values in the majority class. * Hypothetical case study: COVID-19 vaccine misinformation: to illustrate the applicability of our model, consider a hypothetical fake news case claiming that \"alcohol cures COVID-19\". Our proposed system would first analyze the content of the news article. If the content is rich, detailed, and linguistically credible, the system assigns a low probability of the news being fake, indicating it is likely true. However, if the content is shallow or lacks depth, the system assigns a high probability of the news being fake. In such cases, the model further analyzes user comments from multiple platforms, such as Twitter and Reddit, to gain additional insights. For this example, comments might display varying degrees of support or disagreement. Supportive comments might include: (a) \"Finally, an easy cure for COVID! Alcohol every day is the way!\" (b) \"This is amazing! People need to know alcohol can save lives!\"Conversely, non-supportive comments might include:  
* \"This is fake news. Drinking alcohol won't cure COVID-19.\"
* \"Don't trust this claim--it's dangerous and unsupported by science!\"  
If comments across both platforms consistently support or refute the claim, this consistency strengthens the evidence, enhancing the model's confidence in its prediction. For instance, consistent disagreement across platforms would reinforce the conclusion that the news is fake with lower uncertainty. On the other hand, if comments display conflicting patterns--supportive on one platform but refuting on another--the model incorporates high uncertainty. Correlation is calculated to check the consistency between comments of two social media platforms. By integrating content analysis and cross-platform comment evaluations, our system effectively detects fake news while addressing the nuances of cross-domain fake news. This case highlights the robustness of our approach in leveraging both content and user interactions to assess the credibility of news, even in scenarios involving conflicting or ambiguous signals.