## 2 Methodology
### Experimental Procedure
#### 2.3.3 Design Parameter Mapping  
According to the principle of information independence in AD, the key customer attributes (CAs) of elderly users were effectively converted into functional requirements (FRs) of the product, which were subsequently mapped in a zigzag pattern to generate design parameters (DPs). This process establishes a structured parameter framework within the design domain, as shown in Figure 5. It not only enhances the rigor of the design logic but also improves the operability of transforming user needs into functional requirements, thereby ensuring user-friendliness and practical applicability. This study primarily applied the Independence Axiom to ensure that each functional requirement was satisfied by a distinct and independent design parameter. Based on this principle and guided by identified user needs, multiple design solutions were proposed, illustrating a diversified approach to product development within the context of aging-friendly design using AD principles. The solution process for these design parameters is shown in Equations (9) and (10):  
\[\{FR_{s}\}=B\{DP_{s}\} \tag{9}\]  
where the set of functional requirements of the product is denoted as \(FRs\), the set of specific design parameters is denoted as \(DPs\), and the design parameter matrix is denoted as \(B\). The specific expressions are as follows:  
\[\begin{bmatrix}FR_{1}\\ FR_{2}\\ \ldots\\ FR_{n}\end{bmatrix}=\begin{bmatrix}b_{11}&b_{12}&\ldots&b_{1n}\\ b_{21}&b_{22}&\ldots&b_{2n}\\ \ldots&\ldots&b_{ij}&\ldots\\ b_{n1}&b_{n2}&\ldots&b_{mm}\end{bmatrix}\begin{bmatrix}DP_{1}\\ DP_{2}\\ \ldots\\ DP_{m}\end{bmatrix} \tag{10}\]  
where the relationships between the relevant parameters in the matrix are denoted as \(b_{\bar{y}}\).  
In the AD methodology, the design matrix is commonly used to represent the relationships between functional requirements (FRs) and design parameters (DPs). Its structure directly determines whether the Independence Axiom is satisfied, thereby influencing the feasibility and complexity of subsequent design stages. Based on the matrix structure, design matrices are typically classified into three types: uncoupled, decoupled, and coupled designs, as shown in Figure 6. This figure presents standard configurations for each matrix type and explains the symbols used. \"\(X\)\" indicates a strong relationship between an FR and a DP, whereas \"\(O\)\" denotes a weak relationship. In an uncoupled design matrix, matrix A is diagonal, with \"\(X\)\" appearing only on the main diagonal and all other elements as \"\(O\)\". In this case, each FR is independently satisfied by a unique DP without interference, thus fully meeting the Independence Axiom. In a decoupled matrix, A is lower triangular, indicating that some DPs influence multiple FRs. However, by adjusting the implementation sequence, FRs can still be achieved independently. In contrast, a coupled  
Figure 5: Mapping relationships in AD theory.  
matrix features irregularly distributed \"X\" values, where multiple DPs affect multiple FRs, indicating significant coupling and violation of the Independence Axiom. Such matrices typically require redesign to reduce complexity and improve system controllability.