## 3 Design Execution and Result
### Stage 3-Construction of the Preference Models  
After the acquisition of aesthetic values of vase forms, the subjects' preferences for them need to be known as well to construct the preference models. The investigation survey of preferences has been conducted in the way of questionnaire, and is assisted by the 3D vase model attachment. Before the questionnaire was started, the operator especially emphasized that the subjects should exclude extra factors such as the functions of vases, matching with flowers, etc. They should carry out the preference considerations just based on the form of vases. Firstly, subjects were asked to roughly pick their favorite vases from all of the samples, and it was especially defined what the so-called \"favorite\" means: that they are attracted to such a vase at the first view, and want to own it. After that, they were asked to pick the vases from those remaining which are aversive, where \"aversive\" means those vases the subjects do not want to own. Finally, subjects were asked to identify those vases which were not selected during the two steps of \"favorite\" and \"aversive\", i.e., the subjects feel these vases are \"common\" vases based on their feeling. That is, the subjects do not especially like nor dislike these vases, but if there were no better vases, the subjects would still select to own them. The reason for the structure of the selection process is that subjects have a more definite feeling toward extreme values, which are the group of \"favorite\" and \"aversive\". Such a selection method is to ensure the accuracy of the preference classifications. After the rough selections, subjects were then further asked to rank a definite sequence for each segmentation group, which is from relatively like to relatively dislike. This way the ranking of each subject for the preference of all vases can be determined. The reason for firstly carrying out rough preference classifications is to expect a prior compression of the assessment amount for subjects, which makes the final result even more precise. A schematic of this process is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Vase Number** & **Vase Form** & **Symmetry** & **Minimalism** & **Cohesion** \\ \hline
17 & 0.5 & 0.1 & 0.7 \\
18 & 0.4 & 0.5 & 0.6 \\
19 & 0.5 & 0.2 & 0.6 \\
20 & 0.3 & 0.1 & 0.9 \\
21 & 0.5 & 0.5 & 0.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._The preferences of 107 subjects were recorded. The subjects' ranking of these 21 vase samples are respectively recorded as P21-P1, which start from the most liked to the most disliked. Therefore, the relationships between preferences and forms can be understood by means of conjoint analysis. The aesthetic values of Symmetry, Minimalism, and Cohesion of vases and subjects' preference ranking were input into the SPSS syntax of conjoint analysis. The first row of DATA LIST is the definition of data meaning, and it includes the numbers of 1-107, which represent the indices of subjects in the first row. The numbers in the rest of the columns represent the corresponding vase sequences from P21 to P1, which were ranked by each subject; the portions of BEGIN DATA to END DATA are namely the data input, which is the questionnaire result; row 111 is the data of product samples, which contains the aesthetic values of vase forms. This data was saved in advance as a SPSS file format. The data of DISCRETE in row 112 represents the selection of preference models. Since subjects' preference trends in aesthetic principles is still unknown, there is no presumption in this research; thus, each attribute and level will be viewed as a class variable for the implementation; the output storage syntax is in row 118, and the part-worth utilities of result can be obtained. Each subject's part-worth utilities for each aesthetic principle value are known from the results. When the part-worth utility is larger, the degree of influence of theses aesthetic values on subjects' preference ranking (the ranking for a larger P) is higher.