## 2 Materials and Methods
### Analyzing NCMs for Decision Support
#### 2.2.2 Dynamic Analysis of NCMs  
Neutrosophic cognitive representations are a valuable tool for both decision-making and for predicting future situations. With the dynamic analysis of an NCM (Figure 5), we can see the effects and changes brought about by the interactions of the nodes of a system at each step of the process. A dynamic study of an NCM can be used to monitor and evaluate the impact of changes within the decision domain over time. By using the connection matrix and an initial state vector, which represents the input stimulus reflecting the initial conditions or activations of the system's concepts, the resulting state can reveal critical insights into the potential consequences of any alterations made to the system represented by the NCM. These adjustments can be made, for example, by turning a certain notion \"on\" to answer a \"what-if\" inquiry. The algorithm used by the NCM for dynamic analysis is as follows:  
To better comprehend the dynamic analysis procedure, let us first discuss the structure and functioning of a basic NCM. We recall that concept values \(Ci\) take values in \(\{0,1,l\}\) (\(I\) is the indeterminate state) and that causal edges take values in \(\{-1,\ 0,\ 1,\ I\}\). The values \(-1\) and \(1\) indicate complete negative and full positive causality, respectively. Zero indicates no causal effects, I indicates indeterminate causality, and all other values correspond to different neutrosophic degrees. An NCM with \(n\) concept nodes is characterized by an \(n\times n\) connection matrix, E, which contains the causal link strengths (or weights). The previously presented Figure 4 depicted a basic NCM with five concept nodes, while Figure 6 shows the connection or adjacency matrix E in the form of causal linkages between nodes. Figure 5: Algorithm for simulating the interactions of dynamic analysis in an NCM. Figure 6: Adjacency matrix of NCM in Figure 4.  
The \(i_{th}\) row shows the connection strength of the edges \(e_{ik}\) pointed away from the causal concept \(C_{i}\). The \(j_{th}\) column lists the edges \(e_{ki}\) that lead into \(C_{i}\). We say that \(C_{i}\) causes \(C_{k}\) to grow if \(e_{ik}>0\), to decrease if \(e_{ik}<0\), to have no impact if \(e_{ik}=0\), and to have an undetermined effect on \(C_{k}\) if \(e_{ik}=I\). In this way, we observe that the causal concept \(C_{5}\) enhances concepts \(C_{3}\) and \(C_{4}\), but has no effect on concept \(C_{2}\) and an uncertain effect on concept \(C_{1}\). **Definition 9** ([29]). : _Assume \(C_{1}\), \(C_{2}\),... \(n\) to be the NCM's nodes. Let \(A=\) (\(a_{1}\), \(a_{2}\),... \(a_{n}\)) with \(a_{i}\)\(\in\) {0, 1, 1}. A is known as the instantaneous state neutrosophic vector, and it represents the node's on, off, or indeterminate state position at a given moment, i.e., \(a_{i}\)\(=0\) if \(a_{i}\) is off (no effect) \(a_{i}=1\) if \(a_{i}\) is on (has effect) \(a_{i}=1\) if \(a_{i}\) is indeterminate (effect cannot be determined) for \(i=1\), \(2\),..., \(n\)._  
The state vector of an NCM at any time represents a snapshot of the concept values or events in the scenario being modelled. For example, in the NCM depicted in Figure 4, node \(C_{2}\) represents the second component of the state vector. The state [0 1 0 0 0 0] signifies that the notion or concept \(C_{2}\) is active. This state vector may be used as an input value to monitor the impact on every concept over time. The new value for every concept is derived based on the present values of the concepts that impact it through causal relationships. NCMs reach equilibrium when the dynamic system stabilizes. Basic inference criteria for NCMs involve matrix-vector multiplication, as outlined in [45,46]. The state vectors \(C_{n}\) cycle through the NCM adjacency matrix E: \(C_{1}\to E\to C_{2}\to E\to C_{3}\)...