Comprehensive Performance Evaluation of Insulation Materials for Low-Carbon Renovation of Enclosure Structures in Old Communities Based on Cloud Model and Matter–Element Extension Method

The selection of insulation materials during the renovation of enclosure structures in old communities significantly impacts project quality, cost, and carbon emissions. Many insulation materials currently in use only meet energy-saving standards as required by design specifications, often neglecting important aspects such as ancillary construction materials, construction techniques, and environmental protection. Furthermore, they fail to adequately address the unique characteristics of old communities. This study establishes a performance evaluation framework for low-carbon insulation materials in old community enclosures, assessing their suitability from four dimensions: technical performance, economic benefits, social impact, and environmental standards. By introducing the attribute hierarchy model (AHM), subjective weights are determined, while objective weights are obtained using the entropy method and variation coefficient method. A combination of subjective and objective weights are then applied to create a scientific and rational comprehensive evaluation model. The evaluation of insulation materials is conducted using a combination of the matter–element extension method and the cloud model. A case study of a specific old community retrofit project demonstrates that the use of Expanded Polystyrene (EPS) as the insulation material is more suitable for the low-carbon retrofit of the enclosure structures. The results indicate that the proposed evaluation system is both applicable and effective for similar projects.