## 3 Proposed Framework
### Belief Rule-Based Expert System  
A belief rule is an extended form of IF THEN rules. It consists of the antecedent part and consequent part. The antecedent part contains the antecedent attributes and the consequent part that takes the consequent attributes. Referential values are utilized by the antecedent attributes and the belief degrees are connected with the consequent attributes. The relation can be shown as Equation (3):  
\[R_{k}=\left\{ \begin{aligned} & IF(I_{1}\to Q_{1}^{k})\quad AND/OR\quad(I_{2}\to Q_{2}^{k}) \quad AND/OR\_AND/OR\quad(I_{T_{k}}\to Q_{T_{k}}^{k}),\\ &\\ & THEN(O_{1},\beta_{1}),(O_{2},\beta_{2}),...,(O_{n},\beta_{n_{k}}),\end{aligned} \right. \tag{3}\]  
where \(I_{1}\), \(I_{2}\),..., \(I_{T_{k}}\) are the antecedent attributes of \(k\)th rule (\(k\) = 1, 2,..., L). \(Q_{1}\), \(Q_{2}\),..., \(Q_{T_{k}}\) are the referential values. \(O_{1}\), \(O_{2}\),..., \(O_{n}\) are the referential values of the consequent attribute and \(\beta_{1}\), \(\beta_{2}\),..., \(\beta_{n}\) are the belief degree for each referential value, and \(\sum_{j=1}^{n}\beta_{jk}\leq 1\) where attribute weights are \(\delta_{k1},\delta_{l2},\ldots,\delta_{kT_{k}}\), and the rule weight is \(\theta_{k}\). Generally, the group of belief rules is considered as the Belief Rule Base (BRB). In a Belief Rule-Based Expert System (BRBES), it helps to generate the initial knowledge base, and Evidential Reasoning (ER) provides services as an inference engine. Some of the knowledge representation parameters are rule weight [(29)], belief degrees [(30)], and attribute weight [(31)]. These are used to identify uncertainty in data. The inference procedure includes input transformation [(32)], rule activation [(29)], belief update [(33)], and rule aggregation [(34)]. The working process of a BRBES is shown in Figure 4.  
The process of the calculating activation weight, \(w_{k}\), in disjunctive BRB is shown in Equation (4):  
\[w_{k}=\frac{\theta_{k}\sum_{i=1}^{T_{k}}\alpha_{i}^{k}}{\sum_{k=1}^{L}(\theta_{ k}\sum_{i=1}^{T_{k}}\alpha_{i}^{k})}, \tag{4}\]  
where \(\alpha_{i}\) is the matching degree and \(\theta_{k}\) is the rule weight. The process of belief degree update is shown in Equation (5):  
\[\beta_{ik}=\tilde{\beta}_{ik}\times\frac{\sum_{t=1}^{T_{k}}(\tau(t,k)\sum_{j=1 }^{I_{k}}\alpha_{ij})}{\sum_{t=1}^{T_{k}}(\tau(t,k))}. \tag{5}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Content** & **Details** \\ \hline Convolution Layer & 5 layers, 16, 32, 64, 128, and 265 filters of size 2 \(\times\) 2, ReLU, \\  & input shape (150, 150, 1) \\ Max Pooling Layer & 5 layers with pool Size 2 \(\times\) 2 \\ Dropout Layer & 5 layers, Excludes 20\% neurons randomly \\ Global Average Pooling Layer & N/A \\ Output Layer & 6 nodes for 6 classes, SoftMax \\ Optimizer & Adam \\ Callback Function & ModelCheckpoint \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CNN model architecture. The original belief degree is represented by the \(\bar{\beta}_{ik}\), where \(\beta_{ik}\) is the updated belief degree. Rule aggregation is calculated using Equation (6):  
\[\beta_{j}=\mu\times\frac{\prod_{k=1}^{L}(w_{k}\beta_{jk}+1-w_{k}\sum_{i=1}^{N} \beta_{ijk})-\prod_{k=1}^{L}(1-w_{k}\sum_{i=1}^{N}\beta_{ijk})}{1-\mu\times\prod _{k=1}^{L}(1-w_{k})}, \tag{6}\]  
\[\mu=\frac{1}{\sum_{i=1}^{N}\prod_{k=1}^{L}(w_{k}\beta_{jk}+1-w_{k}\sum_{i=1}^{N }\beta_{ijk})-(N-1)\prod_{k=1}^{L}(1-w_{k}\sum_{i=1}^{N}\beta_{ijk})}, \tag{7}\]  
where \(\beta_{j}\) is the ER (Evidential Reasoning) aggregated belief degree. The outputs of the rule aggregation process are some fuzzy values [7]. The process of calculating the crisp value [8] from these fuzzy outputs is shown in Equation (8):  
\[z=\sum_{i=1}^{N}u(S_{i})\times\beta_{i}, \tag{8}\]  
Here, \(u(S_{i})\) is the utility score for each referential value, while \(\beta_{i}\) is ER aggregated belief degree. Figure 5 illustrates the Belief Rule Base Tree of our experiment. X2 which is a root node of this tree represents the \"Overall Sentiment Score\".