# The Application of Fuzzy Theory in the Evaluation of Visual Images of Smartphone Rear Cameras
## 4 Conclusions  
This research applied a consolidated approach of MDS, cluster analysis, questionnaires among experts, factor analysis and fuzzy theory to study the visual images of smartphone rear cameras. Due to the fact that the accuracy of the evaluation samples and image adjectives would have further affected the objectivity and accuracy of the research outcome, we first used MDS and cluster analysis to sort out the representative samples; then through an expert-questionnaire and factor analysis, the image adjectives were efficiently selected. Lastly, triangular fuzzy number operation in the area of fuzzy theory was used to further analyze the visual image evaluations of the smartphone rear cameras. The sample selection method in this study was a scientific technique. This study differed from previous studies in that the samples were converted to 2D images to avoid confounding factors, such as color and brand preference. The study also unpacked the composition of the smartphone rear camera (as shown in Figure 2) so that companies and designers can make better use of the findings of this study. The outcomes show that different shapes of smartphone rear cameras present unique visuals. A total of 11 representative samples had distinct evaluation results in the dimensions of \"innovative and fashionable\" and \"simple and pure,\" but narrow distinctions in the aspects of \"harmonious and ordered,\" \"premium and technical\" and \"superior and valuable.\" Some of the samples contained similarities on the whole; for instance, for S14 and S99, some evaluation results were similar. Therefore, alternatives to those two might be taken into account by phone makers and designers. The results of this research can be applied in the development of new smartphones. For the direction of further research, combining phone size proportion and colors might be considered. The approaches that have been shown in this paper, devised for the acquisition of visual image evaluation values of smartphone rear camera forms, entailed the establishment of an auxiliary design system for smartphones. Matters worthy of consideration are that disparities exist in the lives of users from different countries, which might lead to varied sentimental demands and aesthetic preferences. The participants were all from Taiwan or Mainland China, so they had similar cultural backgrounds. It is also advised that further research may take cultural background as a variate. If the inclination \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Source** & **SS** & **DF** & **MS** & **F** & **P** & **\(\eta\)2** & **LSD** \\ \hline \hline \multirow{8}{*}{
\begin{tabular}{c} Rear cameras \\ (11 samples) \\ \end{tabular} } & \multirow{8}{*}{169.342} & \multirow{8}{*}{10} & \multirow{8}{*}{16.93} & \multirow{8}{*}{10.80} & \multirow{8}{*}{0.000 **} & \multirow{8}{*}{0.89} & \multirow{8}{*}{S14 \(<\) S47} \\  & & & & & & & S27 \(<\) S14, S33, S39, S47, S50, S58, S74, S95 \\  & & & & & & & S99 \\  & & & & & & & S33 \(<\) S39, S47, S74, \\  & & & & & & & S33 \(>\) S27, S49, S49, S59, S99, \\  & & & & & & & S47 \(>\) S14, S27, S33, S49, S50, S58, S74, S95 \\  & & & & & & & S99 \\  & & & & & & & S49 \(<\) S14, S33, S39, S47, \\  & & & & & & & S99 \(<\) S93, S47, \\  & & & & & & & S99 \(<\) S93, S47, \\  & & & & & & & S99 \(<\) S93, S47, \\  & & & & & & & S99 \(>\) S27, S49, S58, \\  & & & & & & & S99 \(>\) S27, S49, S58, \\ \hline \hline \end{tabular}  
* Significantly different at \(\alpha\) = 0.01 level (\(p<\) 0.01).  
\end{table} 
Table 13: The results of the general linear model. towards visual images on the part of users is correctly handled, then smartphones that comply to consumer thoughts and demands can be devised. Conceptualization, Z.L. and C.-H.C.; methodology, Z.L. and C.-H.C.; investigation, Z.L. ; formal analysis, Z.L. ; writing--original draft preparation, Z.L. ; writing--review and editing, C.-H.C.; All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable.