## 5 The Case Study Results and Analysis
### Case Discussion  
The method proposed in this paper was compared with an expert decision-making method that combines the traditional Fuzzy Set and linear superposition methods. The expert decision-making method yielded a ranking result of \(\mathbf{P}_{7}{\rightarrow}\mathbf{P}_{6}{\rightarrow}\mathbf{P}_{8}{ \rightarrow}\mathbf{P}_{2}{\rightarrow}\mathbf{P}_{5}{\rightarrow}\mathbf{P}_{4}{ \rightarrow}\mathbf{P}_{3}{\rightarrow}\mathbf{P}_{1}\). The final scenarios obtained from the two decision-making methods were not the same, so a comparative analysis of \(\mathbf{P}_{6}\) and \(\mathbf{P}_{7}\) was needed.  
\begin{table}
\begin{tabular}{c c c c} \hline  & \(\mathbf{\sigma_{i}}\) & \(\mathbf{\tau_{i}}\) & **Comprehensive Score** \\ \hline P1 & 0.000000 & 0.096770 & 0.046450 \\ P2 & 0.803731 & 0.511047 & 0.663243 \\ P3 & 0.304128 & 0.000000 & 0.158147 \\ P4 & 0.519375 & 0.391177 & 0.457840 \\ P5 & 0.521313 & 0.109288 & 0.323541 \\ P6 & 1.000000 & 1.00000 & 1.00000 \\ P7 & 0.964745 & 0.655082 & 0.816107 \\ P8 & 0.808163 & 0.700402 & 0.756438 \\ \hline \end{tabular}
\end{table}
Table 10: Comprehensive score of crowd-intelligence-driven product form design schemes.  
In the expert decision-making method, \(\mathbf{P}_{7}\) had a composite score of 0.6372 and \(\mathbf{P}_{6}\) had a composite score of 0.6205. \(\mathbf{P}_{7}\) outperformed \(\mathbf{P}_{6}\) in terms of overall evaluation score. However, from the analysis of each evaluation attribute (with relative weightings of \(\mathbf{P}_{7}\) in the order \(w_{4}\)\(\rightarrow\)\(w_{5}\)\(\rightarrow\)\(w_{3}\)\(\rightarrow\)\(w_{2}\)\(\rightarrow\)\(w_{1}\)), it could be observed that \(\mathbf{P}_{7}\) was significantly better than \(\mathbf{P}_{6}\) only in terms of the shapes of the attributes. The color and material attributes were relatively close between the two schemes. In contrast, regarding the relative weight of interactivity and ergonomics, \(\mathbf{P}_{6}\) outperformed \(\mathbf{P}_{7}\). Therefore, \(\mathbf{P}_{6}\) was superior to \(\mathbf{P}_{7}\) from the point of view of a comprehensive comparison of all attributes.  
Meanwhile, the small difference between the scores of \(\mathbf{P}_{6}\) and \(\mathbf{P}_{7}\) was attributed to overlooking the decision-maker's hesitancy during the decision-making process, which led to an absence of certain evaluative information. This also highlights the distinction in the processing of linguistic decision information between traditional Fuzzy Sets and the PHFS. The method proposed in this paper considers the hesitant and ambiguous psychological behavioral characteristics of decision-makers during the decision-making process, particularly in ambiguous decision-making environments where decision-makers may not be fully rational. By retaining more initial decision-making information, this method enables decision-making results to be more objective and better aligned with actual decision-making needs. When dealing with decision language information on product form attributes, the advantage of PHFS lies in its ability to reduce the problem of missing information during the assembly of evaluation information, thereby helping to mitigate product development risks stemming from decision errors.