Abstract: This study develops a validated, disability-inclusive acceptance framework for AI-assisted elder care systems, addressing a critical gap by focusing on the underrepresented perspectives of older adults with disabilities in China. Through a rigorous three-stage methodology, synthesizing aging-technology and disability studies literature, expert co-design with specialists in gerontology, human-computer interaction, AI ethics, and disability advocacy, and participatory piloting, we established a multidimensional framework of six criteria and eighteen sub-criteria. Survey data from 238 elderly participants with visual, hearing, motor, and cognitive impairments across three Chinese cities were analysed using the novel GSRA, TOPSIS for validation, and Kruskal–Wallis H tests for subgroup analysis. Results identify Emergency Response Reliability (GRG = 0.811; "S" _"i"  "=0.719" ; "w" _"i"  = 28.5%) as the paramount trust factor, followed by Interface Simplicity and Voice & Multimodal Interaction Quality. Contextual factors like infrastructure and family support were consistently deprioritized. Importantly, the Kruskal–Wallis test revealed trust perceptions are significantly influenced by disability type (H=18.73, p<0.001), with motor-impaired users placing highest importance on emergency reliability. Strong agreement between GSRA and TOPSIS confirms the robustness of the findings. We conclude that trust is fundamentally built through the AI system's own functional reliability and accessible design, not external conditions. The study offers an evidence-based, culturally informed framework to guide the creation of equitable, trustworthy, and disability-inclusive AI systems for aging populations, contributing to both aging-technology design and the practical application of grey system theory.

Key words: AI acceptance, elderly with disabilities, grey relational analysis, sigmoid analysis, China elder care, aging technology