# The Application of Fuzzy Theory in the Evaluation of Visual Images of Smartphone Rear Cameras
## 3 Results and Discussions
### The Results of Fuzzy Operation
evaluation questionnaire was devised in accordance with the 7-phase fuzzy meaning scale, as shown in Table 2. A total of 155 participants, 72 males and 83 females, were invited for the experiment by using the convenience sampling method. Their ages ranged from 18 to 40 years old. The questionnaire outcome, through the triangular affiliating function, quantified fuzzy meaning into triangular fuzzy numbers. After adding together and averaging, the mean values are shown in Table 10. Then, by the sequence of visual image evaluation samples, the fuzzy triangular diagram was drawn (see Figure 7). The triangular fuzzy number in Table 10, after defuzzification with the absolute utility value formula, produced the absolute utility value of the 11 representative visual image evaluations (Table 11). The detailed calculation is as follows:  
Presume n numbers of triangular fuzzy number in an affiliating function; define it as \(\widetilde{\mathbf{t_{i}}}\)=\((\mathbf{t_{1}},\mathbf{t_{2}},\mathbf{t_{3}})\), i =1,2,..., \(\mathbf{n}\); in this way, the minimum \(\mu_{G}(x)\) and maximum \(\mu_{M}(x)\) are respectively G and M. The absolute utility value of \(\mathbf{U_{T}}\big{(}\widetilde{\mathbf{t_{i}}}\big{)}\) is as Equation 1 shows:  
\[ \begin{array}{l}\mathbf{U_{T}}\Big{(}\widetilde{\mathbf{T_{i}}}\Big{)} =\Big{[}\frac{(\mathbf{T_{B}}-\mathbf{X_{MIN}})}{((\mathbf{X_{MAX}}-\mathbf{ X_{MIN}})+(\mathbf{T_{I3}}-\mathbf{T_{I2}}))}+\mathbf{1}-\frac{(\mathbf{X_{MIN}}- \mathbf{t_{1}})}{((\mathbf{X_{MAX}}-\mathbf{X_{MIN}})+(\mathbf{T_{I2}}- \mathbf{T_{I1}}))}\Big{]}/2,\\ \mathbf{i}=1,2,\ldots,\mathbf{n}\end{array}  \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Innovative and** & **Harmonious and** & **Premium and** & **Superior and** & **Simple and Pure** \\
**Fashionable** & **Ordered** & **Technical** & **Valuable** & **Simple and Pure** \\ \hline S95 (5.0 6.7 9.0) & S47 (4.5 6.4 8.1) & S74 (4.3 6.2 7.8) & S74 (4.5 6.3 7.9) & S47 (4.8 6.6 8.2) \\ S74 (4.2 6.0 7.7) & S74 (4.4 6.3 7.9) & S33 (3.9 5.8 7.5) & S95 (4.0 5.8 7.4) & S39 (4.6 4.8 0.0) \\ S33 (4.0 5.8 7.5) & S39 (4.1 5.9 7.6) & S95 (4.0 5.8 7.4) & S33 (3.6 5.7 3.7) & S14 (4.9 6.8 0.0) \\ S47 (3.7 5.6 7.4) & S33 (3.9 5.7 5.7) & S47 (3.8 5.7 7.4) & S47 (3.6 5.4 7.2) & S99 (4.2 6.0 7.6) \\ S50 (3.8 5.7 2.7) & S50 (3.8 5.6 7.3) & S50 (3.6 5.4 7.1) & S58 (3.6 5.4 7.2) & S50 (4.0 5.8 7.5) \\ S58 (3.6 4.7 7.1) & S14 (3.9 5.6 7.2) & S58 (3.5 5.3 7.1) & S50 (3.2 5.0 6.8) & S74 (3.8 5.7 4.4) \\ S27 (3.9 5.5 7.0) & S99 (3.6 5.4 7.2) & S39 (3.2 1.6) & S27 (3.5 2.6 8.8) & S33 (3.4 5.1 6.8) \\ S49 (3.4 5.1 6.7) & S58 (3.7 5.7 5.2) & S27 (3.5 2.6 6.8) & S99 (2.8 4.6 6.3) & S58 (3.1 4.9 6.7) \\ S14 (3.2 4.8 6.4) & S95 (3.7 5.7 2.2) & S99 (3.2 5.0 6.8) & S49 (2.9 4.6 6.3) & S95 (3.1 4.8 6.6) \\ S99 (3.0 4.7 6.4) & S27 (3.0 4.7 6.3) & S14 (3.4 5.1 6.8) & S14 (2.9 4.5 6.2) & S27 (2.3 3.8 5.5) \\ S39 (2.3 4.0 5.8) & S49 (2.5 4.0 5.7) & S49 (2.9 4.5 6.2) & S39 (2.5 4.2 6.0) & S49 (2.0 3.5 5.3) \\ \hline \end{tabular}
\end{table} 
Table 10: The sequence and means of the visual evaluations of the samples of the smartphone rear cameras. Figure 7: The triangular fuzzy numbers of the 11 representative samples in each visual evaluation. The above results state:  
In Figure 7, it is shown that different smartphone rear cameras received different visual evaluations in the categories of \"fashionable and technical\" and \"superior and valuable\"; yet in the categories of \"premium and technical\" and \"superior and valuable\", the distinctions were limited. As shown in Table 10 statistics, sample S14 received the highest grades in the evaluation for the category \"simple and pure\"; sample S47 received high grades in categories \"harmonious and ordered\" and \"simple and pure\"; sample S74 received great grades in each evaluation, achieving its best grades in \"premium and technical\" and \"superior and valuable\"; sample S95 received good grades except in \"superior and valuable\", and its highest grade appeared in the evaluation of \"superior and valuable\".