## 2 Theoretical Background  
### Fuzzy Theory  
Fuzzy theory is a subject of science that deals with the study and processing of fuzzy phenomena. It was proposed in 1965 by [PERSON], an expert in control theory at the University of California, Berkeley, USA. It has been a subject for more than 40 years and has been used for processing imprecise data with vagueness. With rigorous mathematical methods for calculation, the strategic problems under a fuzzy environment can be resolved by this approach [14]. During design assessment, there are many targets, such as aesthetics (overall effect, shape, color, decoration, etc.), amenity, safety, machinability, etc. These targets are difficult to determine by conventional quantitative analysis. Therefore, linguistic variables must be introduced for description in order to acquire a solution. After that, the fuzzy mathematical approach can be used to numerate the fuzzy information for quantitative evaluation.  
[PERSON] utilized fuzzy theory and hierarchical analysis to carry out strategic decisions [25] and utilized fuzzy theory to evaluate monochromatic color schemes during the car appearance design phase [27; 28]. In addition, he also applied fuzzy semantics to the strategic decision of automobile shape designs [21; 22]. Moreover, the semantic transformation from adjectives was applied to the design of product forms in order to carry out computer-aided industrial design and assess form images [29; 30].  
In addition, a number of scholars have also proposed different computer-aided systems to assist designers and engineers in reducing the time for research and development and document processing. In 1997, [PERSON] and [PERSON] proposed a decision support system with optimal product designs [31]. [PERSON] et al. proposed a deduction framework in 1999 in order to deduce the relationship between customer requirements (CRs) and design requirements (DRs) [32]. However, the knowledge and experience of experts are required to construct the rules when developing this type of system. At the same time, designers also encounter problems whether a system is in good operation or not. According to fuzzy set theory, [PERSON] et al. utilized data, such as the analysis of the competitiveness of companies, to construct a correlation function between CRs and DRs. They proposed a fuzzy multi-objective model. However, it is difficult to build this correlation function. This is especially true when developing a brand-new product without any data from competitors for analysis [33]. Other scholars have applied fuzzy sets, fuzzy algorithms, or defuzzification techniques to process complex and imprecise quality function deployment problems. However, these methods do not take into account the relationships between engineering design demands. Other scholars have emphasized that the quality function deployment needs to not only determine the performance based on customer satisfaction but also consider organizational criteria such as cost factors and technical difficulties so as to determine the optimal decision that is economical and satisfactory for customers.  
Among various targets of a design, some required concepts are definite while others are vague. It is also required to consider several targets and comprehensively consider various relevant factors and carry out comprehensive assessments. This is the so-called fuzzy comprehensive assessment. The process of implementing fuzzy assessment includes constructing the affecting factor set, determining the factor weight set, determining the parameter evaluation set, creating the single-factor assessment matrix, and conducting the fuzzy evaluation. These procedures are described as follows: