## 4 Results
This mapping is founded on three pillars: (1) our preliminary imagery-evaluation experiments demonstrated stable correlations between form features and user perceptions--for example, symmetrical, block-like shapes are consistently rated as \"steady,\" whereas strongly curved, complex line configurations evoke \"agile\" or \"technological\" impressions; (2) empirical findings in design-perception research ([PERSON] et al. [33] showed that contour symmetry and structural repetition significantly enhance perceptions of \"stability\" and \"product-quality credibility,\" while [PERSON] et al. [34] linked nonlinear paths and sharp angles to \"technological\" and \"futuristic\" sensations); and (3) the inherent semantic affordances of transformation rules themselves--for instance, mirroring (R7) and duplication (R6) foster symmetry and order aligned with \"steady\" and \"modern\" styles; shearing (R8) and fine-tuning (R3) introduce local tension and nonlinearity suitable for \"technological\" or \"agile\" expressions; and subtraction (R2) and replacement (R1) emphasize streamlined forms serving \"minimalist\" or \"elegant\" intents. Based on these three criteria, an imagery-to-rule mapping matrix was constructed (Table 10) to serve as a decision-support tool for imposing stylistic constraints on shape grammar-based variant generation. The primary variants of the four key path elements (L\({}_{1}\)-L\({}_{4}\)) were designated as factors A-D, each at four levels, and arranged into 16 experimental combinations using an L\({}_{16}\)(4\({}^{4}\)) orthogonal array. The experimental plan was generated and the corresponding schematic sketches were produced in SPSS (Figure 13). Following the generation of 16 design variants, we applied grey relational analysis (GRA) for multi-criteria evaluation and selection of prototypical styles. First, five experts rated each variant on six perceptual dimensions--\"steady,\" \"modern,\" \"technological,\" \"agile,\" \"minimalist,\" and \"elegant\"--to construct the evaluation matrix. The data were then range-normalized, and grey relational coefficients were calculated against an ideal reference sequence comprised of each dimension's maximum value (distinguishing coefficient \(\rho=0.5\)). Finally, weighted grey relational grades were computed using interval weights derived from prior Extenics analysis (w = [0.186, 0.166, 0.166, 0.166, 0.159, 0.157]) and ranked in descending order. The results (Table 11) identify Variant 16 as having the highest grey relational grade, thus selected as the representative design sample. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Imagery** & \begin{tabular}{c} **Typical Form** \\ **Semantic Features** \\ \end{tabular} & **Primary Rules** & **Secondary Rules** & **Constraint Rules/Notes** \\ \hline \multirow{2}{*}{Sturdy} & Strong symmetry, sense of & R6 Duplicate, R7 Mirror & R4 Scale & \begin{tabular}{c} Avoid R8 Shear to \\ maintain solidity \\ \end{tabular} \\ \hline \multirow{2}{*}{Tech} & Sharp, dynamic, & R3 Fine-tune, R8 Shear & R3 Add/Delete, R5 Rotate & \begin{tabular}{c} Restrict R6 Duplicate to \\ prevent redundancy \\ \end{tabular} \\ \hline \multirow{2}{*}{Agile} & Asymmetric, zigzag, high & R1 Replace, R2 & R3 Fine-tune & \begin{tabular}{c} Restrict R6 Duplicate and \\ R7 Mirror \\ \end{tabular} \\ \hline \multirow{2}{*}{Minimal} & Geometric, few lines, & R1 Replace, R2 Delete & — & \begin{tabular}{c} Avoid complex transforms \\ (e.g., R5, R8) \\ \end{tabular} \\ \hline \multirow{2}{*}{Modern} & Clear modules, balanced & R4 Scale, R6 Duplicate & R3 Fine-tune & \
\begin{tabular}{c} Restrict R8 Shear and R1 \\ Random path changes \\ \end{tabular} \\ \hline \multirow{2}{*}{Elegant} & Streamlined, smooth lines, & R1 Replace, R3 Fine-tune & R4 Scale &
\begin{tabular}{c} Avoid sharp angles and \\ shear (R8) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Mapping strategies for emotional imagery and shape rules.