A quantitative framework for translating architectural heritage into cultural product design through ancient theatrical stages in Shanxi

This study proposes a quantitative design transformation framework to revitalize Shanxi’s historical opera stages by aligning heritage semantics with consumer needs. A multi-criteria decision-making model integrating architectural meme theory, AHP, QFD, TOPSIS, and Stable Diffusion was employed. Cultural ‘genes’ extracted from 3D scans formed a meme lineage, where AHP and QFD quantified attributes to guide generative design, and TOPSIS facilitated performance evaluation. Of the resulting cultural products, the “Spire-Top Penholder” yielded the highest relative affinity coefficient, successfully balancing structural authenticity with modern utility. The study confirms that reinterpreting elements like flying eaves through product semantics augments the public perception of heritage value. This study proposes a data-driven paradigm for sustainable heritage preservation, providing a scalable framework for integrating historical architecture into digital platforms for cultural documentation, interpretation, and dissemination.