# Study on Imagery Modeling of Electric Recliner Chair: Based on Combined GRA and Kansei Engineering
## 3 Materials and Methods
### Proximity of Gray Relational Space  
The gray relational analysis method is applied to the sample data of each styling design element, and the strength of the relationship is expressed by the gray correlation coefficient. By comparing the values of these coefficients, a hierarchical order of influence of the different styling design elements on the product image can be established. This process allows us to identify the design elements within the styling that have the greatest impact on the product image. As a result, product designers can pay more attention to these pertinentdesign elements, while de-emphasizing those that are less relevant. The modeling form elements with the most significant impact are selected as linguistic input variables for the fuzzy logic model of gray relational analysis (GRA), with the product image serving as the output variable [53; 54; 55]. Fuzzy logic, a versatile tool for deciphering relationships within subjective fuzzy information systems, has found wide-ranging applications in various domains. Research outcomes have demonstrated that fuzzy logic is adept at handling existing fuzzy information to effectively explore previously unknown associations. It furnishes an efficient system for the modeling of the decision language associated with human perception. Notably, fuzzy logic exhibits robust reasoning capabilities, enabling the emulation of the non-linear and imprecise facets of human brain information processing, thus furnishing an effective decision-making mechanism for the modeling of human language understanding. In the context of product design, where a user's perception of a product image is subjective and inherently fuzzy, the utilization of fuzzy logic models proves highly advantageous in representing the product shape design process. These models describe the shape design elements as input variables and their correlation with the user's perception of the product image, which serves as the output variable. Empirical studies have underscored that fuzzy logic models, particularly those based on fuzzy rules, exhibit superior predictive performance compared to traditional regression models [56]. This paper employs fuzzy logic methods to investigate the relationship between seat modeling elements and the resultant product image, with a focus on addressing the specific design requirements of an electric recliner chair. Electric recliner chairs represent a critical aspect of chair design due to their diverse shapes and designs. Prior research has indicated the complexity of generating and assessing fuzzy rules through conventional research approaches in the realm of seat shape design. Consequently, a novel GRA fuzzy logic method is introduced to systematically construct a set of fuzzy rules grounded in a user-oriented perceptual engineering research methodology. This innovative approach is particularly well-suited for product modeling systems characterized by multiple input variables (product modeling elements) and multiple output variables (product images). In fuzzy theory, the use of triangular fuzzy functions is a valuable approach that can effectively encapsulate domain knowledge within an expert system while significantly streamlining the computational process. Triangular fuzzy functions are a widely used method of representing sets of fuzzy numbers. Triangular fuzzy numbers, denoted as (a, b, c), provide a means of providing approximate ranges for language categories. In this representation, 'b' represents the most likely value for the language item, while 'a' and 'c' serve as lower and upper bounds, respectively. These lower and upper limits reflect the inherent fuzziness or uncertainty associated with the language item, making triangular fuzzy functions a versatile tool in dealing with such linguistic ambiguity [57]. In partnership with the product image database, the ongoing process involves the formulation of fuzzy rules for the GRA fuzzy logic model.