## 3 Detailed Design of Automotive Interior CMF
### Kansei Data Analysis
#### 3.3.2 Establishing the Mapping Relationship between the CMF Design Elements and Kansei Words  
To determine the influence of the CMF design elements on the prominent Kansei words, Quantification Theory I was adopted. The theory can be used to perform quantitative research on problems that are difficult to quantify, and thus could examine the relationship between things more comprehensively [33; 34]. The theory could establish the relationship between a set of independent and dependent variables. After quantifying the qualitative variables into quantitative data of 0 and 1, multiple linear regression is then used to establish the mathematical relationship between the two variables, which is to achieve the goal of predicting the dependent variables. In the Quantification Theory I, the design factors were set as category, and the design elements under each design factor were set as subcategory. Assuming the first category \(X_{1}\) has a number of \(r_{1}\) subcategories, i.e., \(X_{11}\), \(X_{12}\),......., \(X_{1\text{r}1}\), the second category \(X2\) owns a number of \(r_{2}\) subcategories, i.e., \(X_{21}\), \(X_{22}\),......., \(X_{2\text{r}2}\), and the category \(X_{\text{m}}\) owns a number of rm subcategories, i.e., \(X_{\text{m}1}\), \(X_{\text{m}2}\),......., \(X_{\text{m}rm}\), a total number of \(\sum\limits_{j=1}^{m}r_{j}=p\) subcategories were involved. The symbol \(\delta_{i}k(\text{j},\text{k})\)\(\big{(}i=1,\ldots\ldots,n;j=1,2,\ldots,m;k=1,2,\ldots\ldots,r_{j}\big{)}\) represents the response values of the \(k\)th subcategory from the \(j\)th category in the \(i\)th sample, and the values were taken as Equation (1). \[\delta_{i}k(\text{j},\text{k})= \begin{cases}1,&\text{When the qualitative data of the $j$th category in the $i$th sample is the $k$th subcategory}\\ 0,&\text{Others}\end{cases}  \tag{1}\]  
An order matrix of \(n\times p\) was constituted from all \(\delta_{i}k(\text{j},\text{k})\), forming the response matrix, listed in Equation (2)  
\[\delta_{i}k(j,k)= \begin{bmatrix}\delta_{1}(1,1)&\ldots&\delta_{1}(1,r1)& \delta_{1}(2,1)&\ldots&\delta_{1}(2,r2)&\delta_{1}(m,1)&\ldots&\delta_{1}(m, rm)\\ \delta_{2}(1,1)&\ldots&\delta_{2}(1,r1)&\delta_{2}(2,1)&\ldots&\delta_{2}(2,r2)&\delta_{2}(m,1)&\ldots&\delta_{2}(m, rm)\\.&.&.&.&.&.&.&.&.\\.&.&.&.&.&.&.&.\\.&.&.&.&.&.&.&.\\.&.&.&.&.&.&.&.\\.&.&.&.&.&.&.&.\\ \delta_{n}(1,1)&\ldots&\delta_{n}(1,r1)&\delta_{n}(2,1)&\ldots&\delta_{n}(2,r2 )&\delta_{n}(m,1)&\ldots&\delta_{n}(m,rm)\end{bmatrix}  \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Perceptual Words**} & \multicolumn{3}{c}{**Components**} \\ \cline{2-4}  & **1** & **2** & **3** \\ \hline Complex vs. concise & 0.199 & 0.636 & 0.195 \\ Hard vs. soft & \(-\)0.109 & 0.149 & 0.824 \\ Rough vs. graceful & 0.443 & 0.637 & \(-\)0.290 \\ Traditional vs. technological & 0.041 & 0.814 & 0.171 \\ Fragile vs. durable & 0.538 & 0.090 & 0.639 \\ Afflective vs. comfortable & 0.725 & 0.299 & \(-\)0.263 \\ Cold vs. warm & 0.617 & \(-\)0.082 & \(-\)0.562 \\ Polutional vs. environmentally friendly & 0.565 & 0.292 & 0.041 \\ Dangerous vs. safe & 0.777 & 0.109 & 0.112 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Component score matrix. The relationship between the values of the perceptual words (\(y\)) and the design elements could be established, showing in Equation (3). \[y=\sum_{\mathrm{j=1}}^{m}\sum_{\mathrm{k=1}}^{\mathrm{n}}\delta_{\mathrm{i}}k( \mathrm{j,k})b_{\mathrm{j,k}}+\varepsilon_{\mathrm{i}}\quad(\mathrm{i=1,2,\ \ldots,n}) \tag{3}\]  
where \(b_{\mathrm{j,k}}\) only depends on the undetermined coefficient of the \(k\)th design element in the \(j\)th design factor, and \(\varepsilon_{\mathrm{i}}\) is the random error of the \(i\)th sampling. Based on Figure 5 and Equation (2), the response matrix of the 33 samples was obtained. The matrix of the design elements was regarded as the independent variables, and the five perceptual words discussed above was set as the dependent variables.