# The Application of Fuzzy Theory in the Evaluation of Visual Images of Smartphone Rear Cameras
## 2 Materials and Methods
### Visual Image Opinions in Fuzzy Operation  
Fuzzy theory is a scientific approach for the research and treatment of obscure phenomena, and was first put forward by [PERSON] in 1965 [26]. [PERSON] held that humans' ideas, deductions and awareness of matters are substantially ambiguous in themselves. It is therefore necessary to apply fuzzy and logical concepts to describe priority degrees of matters. Through the membership function, it is possible to quantize subjects' inner feelings, converting feelings into numerical values between 0 and 1, where the value denotes the potential influential factors and their respective impacts [26; 27; 28].  
Fuzzy theory, in the application of meaning measuring, is an optimum approach for research. Nowadays, there are numerous design studies that have adopted fuzzy theory [13; 29; 30]. These studies usually adopt fuzzy numbers, of which the regular types are triangular fuzzy number, trapezoidal fuzzy number and normal fuzzy number, of which the triangular fuzzy number is the most common. What is special about the triangular fuzzy number is its affiliated function. The distribution of probabilities is in the form of a triangle [31]. Presuming one triangular fuzzy number int function \(\mu_{i}(x)\), it is \(t=(t_{1},t_{2},t_{3})\), when \(t_{1},t_{2}\), and \(t_{3}\) is a real number and \(t_{1}\leq t_{2}\leq t_{3}\). This affiliated function is shown in Figure 3 [32].  
This research study takes fuzzy meanings of seven grades as the ranking approach (see Table 2). Users were asked to rank the representative samples. The fuzzy ranking results were achieved by the 7-grade triangular affiliating function, making fuzzy meanings triangular fuzzy numbers after quantization. The triangular affiliating function is shown in Figure 4.  
Figure 3: Membership function of a triangular fuzzy number.  
For further analysis and comparison, defuzzification triangular fuzzy numbers in the affiliating function result in crisp values. The maximizing set and minimizing set method, put forward by [PERSON] in 1985 [33], is the most common method for defuzzification and was adopted in this research. The principle is to make use of weights of two triangular fuzzy numbers to restore them to total utility values.  
The questionnaire adopted in this research study was designed based on the fuzzy meaning principle. The questionnaire was administered with a 7-point Likert scale with 11 samples paired with five groups of factors; e.g., how would you rate sample S14 regarding being innovative and fashionable? How would you rate sample S14 regarding being harmonious and ordered? How would you rate sample S14 regarding being premium and technical? How would you rate sample S14 regarding being superior and valuable? How would you rate sample S14 regarding being simple and pure? This helped to identify the consumers' opinions on 11 rear camera samples. After defuzzification of the outcome, the total utility value of each form of visual image was obtained, diagrams and charts were drawn up and further analysis was performed on the 11 samples. The outcomes can provide insights for phone makers, designers and users.