## 4 Results
### Interpretative Structural Modeling  
The ISM approach, which reveals intrinsic logical relationships between influencing factors, has been used in supply chain resilience research in several other areas. Previous \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Variable** & **Std. Estimate** & **AVE** & **CR** \\ \hline \multirow{4}{*}{Intuitiveness} & d1 Operate naturally & 0.783 & & \\ \cline{2-6}  & d2 Metaphorical & 0.768 & & \\ \cline{2-6}  & d3 Cultural meaning & 0.724 & & \\ \cline{2-6}  & d4 Use habits & 0.796 & & \\ \hline \multirow{4}{*}{Attractiveness} & e1 Interface quality & 0.819 & & \\ \cline{2-6}  & e2 Customize & 0.814 & & \\ \cline{2-6}  & e3 Interesting & 0.769 & & \\ \cline{2-6}  & e4 Novelty & 0.785 & & \\ \hline \multirow{4}{*}{Tiredness} & f1 Fatigue & 0.838 & & \\ \cline{2-6}  & f2 Strenuous & 0.872 & & \\ \cline{2-6}  & f3 Comfort & 0.874 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._  
Figure 3: Model result diagram. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model Fit Index** & \(x^{2}\)**/df** & **RMSEA** & **NFI** & **NNFI** & **IFI** & **TLI** & **CFI** \\ \hline Standard value & \(<\)3 & \(<\)0.10 & \(>\)0.9 & \(>\)0.9 & \(>\)0.9 & \(>\)0.9 \\ value & 1.772 & 0.050 & 0.918 & 0.958 & 0.962 & 0.958 & 0.962 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of model fit analysis. studies have shown a relationship between six elements. Any system \(S\) consists of two or more interlinked, interacting elements \((S_{1},S_{2},\ldots S_{n})\), resulting in an organic whole. Through the previous analysis, we can see that there are six factors influencing the satisfaction of mid-air gesture, so six factors \((S_{1},S_{2},\ldots S_{6})\) are selected to establish the set of influencing factors \(S\):  
\[S=\{S_{1},S_{2},\cdots S_{n}|2\leq n\leq 6\}=\{\text{Simplicity, Efficiency, L, Tiredness}\} \tag{1}\]  
Thereafter, we further discussed with experts how to study a reasonable structural relationship and quantify the relationship between factors affecting gestures. It was proposed to use the form of adjacency matrix \(A\) to represent the mutual correlation between them, which is defined in the following way:  
\[A=\left(a_{ij}\right)_{n\times n} \tag{2}\]  
\[\alpha_{ij}= \begin{cases}1,\ S_{i}RS_{j}\\ 0,\ S_{i}RS_{j}\end{cases}  \tag{3}\]  
where 1 indicates that there is a path between one element and another and 0 indicates that there is no path between one element and another. Thus, it is possible to establish an adjacency matrix based on Equations (2) and (3) for the factors influencing the satisfaction of air gestures:  
\[A_{6\times 6}= \begin{bmatrix}0&1&1&0&1&1\\ 1&0&0&0&0&1\\ 0&0&0&0&0&1\\ 1&0&0&0&0&0\\ 0&0&0&0&0&0\\ 1&0&1&0&0&0\end{bmatrix} \]  
The reachability matrix refers to any transitive binary relationship between factors, and a square matrix that represents the relationship between two nodes that can be reached through any path length in a directed graph. Let I be a unit matrix of the same order as \(A\). By the neighborhood matrix \(A\), adopt the Boolean algebra algorithm [71] (i.e., \(0+0=0\), \(0+1=1\), \(1+0=1\), \(1+1=1\), \(0\times 0=0\), \(0\times 1=0\), \(1\times 1=1\)). The corresponding reachable matrix \(M\) is obtained as follows:  
\[M=\left(A+I\right)^{r} \tag{4}\]  
The reachable matrix \(M\) is obtained according to Equation (4):  
\[M= \begin{bmatrix}1&1&0&1&1\\ 1&1&0&1&1\\ 1&1&1&0&1&1\\ 1&1&1&1&1&1\\ 0&0&0&0&1&0\\ 1&1&1&0&1&1\end{bmatrix} \]  
Based on the reachable matrix \(M\), it is possible to calculate the reachable and antecedent sets and the intersection of each influencing factor and obtain the hierarchical results, as shown below:  
\[L1=\{S_{5}\}\]  
\[L2=\{S_{1},S_{2},S_{3},S_{6}\}\]  
\[L3=\{S_{4}\}\]  
Accordingly, it is possible to map out the explanatory structure model of the factors influencing the gesture satisfaction, as shown in Figure 4:Through ISM model analysis, it was found that six factors can be classified into three hierarchical relationships.