# Research on Optimized Product Image Design Integrated Decision System Based on Kansei Engineering
## 3 Product Image Design Integrated Decision System
### Product Image Design Qualitative Decision Model  
#### 3.1.1 Quantification Theory Type I  
The qualitative decision model of product image design is to identify the main design elements affecting product image by quantitative analysis method. The experimental subjects in Section 2 are divided into four groups. The third group is composed of the professional product designers with rich experience in product design. Through the investigation and statistics of professional designers, the four design elements (product form, color, material and texture) are selected for further research of qualitative decision model. Quantification Theory Type I is the method that studies the relationship between a set of qualitative variables \(x\) (independent variables) and a set of quantitative variables \(y\) (dependent variables) [10]. The mathematical model between variables is built up by multiple regression analysis. According to the mathematical model of Quantification Theory Type I, the procedure for establishing the Kansei-associated model is as follows:  
* The mathematical formula of the Kansei-associated model is defined. The product design element is taken as the independent variable \(x\) (qualitative variable) and the Kansei evaluation value is taken as the dependent variable \(y\) (quantitative variable). The purpose of Quantification Theory Type I is to solve the regression coefficient of each design element [11]. Therefore, the multiple regression equation of the product design element and Kansei evaluation value can be defined as: \[\hat{y}_{s}^{k}=\sum_{i=1}^{D}\sum_{j=1}^{M_{i}}\beta_{ij}x_{ij}\] (1) where \(k\) represents the \(k\)th Kansei image, \(k=1,2,\ldots,m\), and \(m\) represents the number of Kansei images; \(s\) represents the \(s\)th experimental sample, \(s=1,2,\ldots,n\), and \(n\) represents the number of experimental samples; \(i\) represents the \(i\)th design element, \(i=1,2,\ldots,D\), and \(D\) represents the  
Figure 4: The Kansei Engineering experiment process of product image design. number of design elements; \(j\) represents the \(j\)th category of the \(i\)th design element, \(j=1,2,\ldots,M_{i}\), and \(M_{i}\) represents the number of category for the \(i\)th design element. \(\hat{y}_{s}^{k}\) is the evaluation value of the \(k\)th Kansei image for the \(s\)th experimental sample. \(x_{ijs}\) represents the independent variable of the \(j\)th category of the \(i\)th design element for the \(s\)th experimental sample, so \(x_{ijs}\) can be defined as follows: \[x_{ijs}=\left\{ \begin{array}{ll}1&\mbox{\it the $j$th category of the $i$th design element } \mbox{\it for the $s$th experimental sample}\\ 0&\mbox{\it otherwise}\end{array} \right.\] (2) And \(x_{ijs}\) meets the condition of \(\sum\limits_{j=1}^{M_{i}}x_{ijs}=1\), \(for\)\(\forall i\) and \(s\). \(\beta_{ij}\) represents the partial regression coefficient of the \(j\)th category of the \(i\)th design element. * Using the least-squares method, error equation can be defined as below: \[Q=\sum\limits_{s=1}^{n}\left(y_{s}^{k}-\hat{y}_{s}^{k}\right)^{2}\] (3) where \(Q\) is the sum of square error between the predicted value and the actual value. In order to improve the prediction accuracy and minimize the error, the following equation can be defined for the calculation of partial differential: \[\frac{\partial Q}{\partial\beta_{ij}}=0,\mbox{ \it for $\forall\beta_{ij}$}\] (4) \(\beta_{ij}\) can be obtained by the simultaneous equations. Namely, the partial regression coefficient of design element can be acquired. The influence degree of each design element on the Kansei image can be obtained by analyzing the numerical value of \(\beta_{ij}\). * The complex correlation coefficient \(R\) can measure the accuracy of the model. Generally, the square of the complex correlation coefficient \(R\), namely, the coefficient of determination \(R^{2}\) is used to represent the accuracy of the model.