## 2 Materials and Methods
### Explainability-Enhancing Methods  
#### 2.3.1 Self-Explainable Aspects of DeepFCM  
At the core of an FCM lies the weight table [10], a fundamental component that defines the strength of relationships between interconnected concepts. The weight table serves as a quantitative representation of domain knowledge and expertise, either contributed by domain experts or inferred from historical data [14]. Each element in the weight table specifies the degree of impact that one concept exerts on another, reflecting the causal influence in the cognitive mapping.  
The weight table's explainable nature stems from its intuitive and comprehensible structure. Domain experts can easily comprehend the impact of each concept on others, as the weight values are interpretable and can be expressed in linguistic terms, such as \"strong\", \"weak\", \"positive\", or \"negative\". This transparency facilitates expert involvement in model development and validation, providing a valuable opportunity to refine and  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Relationship among Concepts** & **Linguistic Value Provided by Experts** \\ \hline Known CAD\(\rightarrow\)Output & S \\ Previous PCI\(\rightarrow\)Output & W \\ Diabetes\(\rightarrow\)Output & S \\ Chronic Kidney Disease\(\rightarrow\)Output & W \\ Angina Like\(\rightarrow\)Output & S \\ ECG\(\rightarrow\)Output & M \\ Male\(\rightarrow\)ECG & W \\ Expert Diagnosis\(\rightarrow\)Output & VS \\ CNN\(\rightarrow\)Output & S \\ \hline \hline \end{tabular}
\end{table}
Table 1: Representation of the suggested weights between meaningful input–input concepts and input–output concepts obtained from nuclear experts.  
fine-tune the model based on domain-specific insights. Furthermore, the weight table's transparency fosters the detection of influential concepts, as high weights indicate strong causal connections. This feature becomes particularly relevant in critical applications such as medical diagnosis, where identifying significant factors affecting the outcome is essential for effective decision making.  
Another critical aspect contributing to the inherent explainable nature of FCMs lies in their representation of interconnections between concepts. The directed edges between nodes in an FCM indicate the causal relationships and the direction of influence from one concept to another. These connections represent the cause-and-effect dependencies that govern the dynamics of the system under consideration. By visually examining the graph structure of the FCM, domain experts can identify complex causal pathways, feedback loops, and interdependencies between concepts. This understanding not only enhances the model's transparency but also facilitates the identification of potential bottlenecks, vulnerabilities, or reinforcing factors within the system. Moreover, the causal relationships depicted by the interconnections in FCMs allow for \"what-if\" analyses, where experts can assess the impact of hypothetical changes to specific concepts on the overall system behavior. Such analyses promote risk assessment and strategic decision making in various applications, including policy planning, environmental management, and healthcare interventions.  
In comparison to other complex ML models, FCMs offer several distinct advantages in terms of interpretability [28]. Neural networks, for example, are notorious for their black-box nature, as the intricate relationships within their hidden layers are challenging to unravel. In contrast, FCMs' explicit representation of causal connections fosters a holistic understanding of the decision-making process, enabling domain experts to assess model predictions with confidence and identify any potential biases or anomalies. Similarly, decision trees, although interpretable, may lack the expressive power to capture complex and uncertain relationships among variables. FCMs, however, excel at dealing with such complexities through the use of fuzzy logic, allowing for continuous and gradable influence between concepts [10].