## 3 Method
### Evaluation of 15-min Walkability to Elderly Care Facilities
#### 3.3.2 Calculation of Walkability Score Based on Optimization Cumulative Opportunity Method  
The walkability assessment method is rooted in the theory of cumulative opportunity accessibility, a framework pioneered by [PERSON] [76] in the mid-20 th century. With advancements in spatial analysis technology, scholars have proposed various improved models: [PERSON] [77] explored the measurement and application of accessibility in transportation  
Figure 3: Facility Service Diagram.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**First Level Indicators** & **Second Level Indicators** & **First-Level Weight** & **Local Weight** & **Global Weight** \\ \hline \multirow{4}{*}{Finance} & Bank & & 0.76686 & 0.01335 \\  & ATMs & 0.0174 & 0.14601 & 0.00254 \\  & Insurance & & 0.08712 & 0.00152 \\ \hline \multirow{2}{*}{Government} & Government organs & & 0.75423 & 0.21532 \\  & Social organization & & 0.24577 & 0.07016 \\ \hline \hline \end{tabular}
\end{table}
Table 5: _Cont._planning [78], [PERSON] et al. [79] introduced a spatial equity correction coefficient, and [PERSON] and [PERSON] [80] validated the method's universality in public service evaluation through empirical research. Building on the classic cumulative opportunity method, this study integrates a static decay function to construct a spatial decay correction model. Based on research on the walking behavior characteristics of the elderly [58], a segmented decay function is designed:  
\[\mathrm{F(m)}=\left\{\begin{array}{cl}1&0<m\leq 5\\ 0.6&5<m\leq 10\\ 0.25&10<m\leq 15\end{array}\right. \tag{1}\]  
The variable m denotes the walking time from a senior care facility to a nearby amenity. The decay function parameters are designed to reflect the walking tolerance characteristics of elderly populations: No decay (full-service zone) within 5 min, partial decay (transition zone) between 5 and 10 min, rapid decay beyond 10-15 min, which aligns with the nonlinear decline in walking speed as distance increases, a physiological pattern observed in older adults.  
A multi-level weighted evaluation model is established as follows:  
\[\mathrm{O_{j}=\sum_{k=1}^{n}\sum_{\mathrm{i=1}}^{m}W_{k}\times N_{i}\times F(m)} \tag{2}\]  
\[\mathrm{O=\sum_{j=1}^{m}O_{j}\times W_{j}\times\frac{O_{j}-O_{jmin}}{O_{jmax}-O _{jmin}}\times 100} \tag{3}\]  
In Equation (2), \(\mathrm{O_{j}}\) represents the score of the category of primary indicator facilities, \(\mathrm{N_{i}}\) is the number of ith category secondary indicator facilities, \(\mathrm{W_{k}}\) is the local weight of the kth category service facilities, and \(\mathrm{F(m)}\) is the attenuation coefficient corresponding to the walking time distance.  
In Equation (3), \(\mathrm{O}\) is the total standardized walkability score of the senior care facility, \(\mathrm{W_{j}}\) is the global weight of the jth category primary indicator, \(\mathrm{O_{jmin}}\) and \(\mathrm{O_{jmax}}\) are the global maximum and minimum scores of the jth category service, respectively.  
This standardization process effectively eliminates dimensional differences, ensuring the comparability of multi-source indicators.