## 2 Detection Methodology
### Calculation of Design-Weighting  
Once we have collected the emotional information of the homeowner regarding indoor environmental elements through the PANAS questionnaire, we can determine the design-weighting of each indoor environmental element. The Entropy Weight method (EWM), introduced by [PERSON] in 1948, is a widely used weighting approach for measuring valued dispersion in decision-making. The wider the distribution, the broader the distinction, and the more information may be extracted. The index must be given more weight, and conversely [20]. Based on the concept of the Entropy Weight method, we have created a new weighting calculation approach for applications within the field of interior design. The calculation procedure of design-weighting on indoor environmental elements (as shown in Table 3) is as follows:  
Step 1: Calculate P\({}_{\text{x-total}}\), which is the sum of positive affects (i.e., P1 + P2\(\ldots\) + P10) expressed by a specific indoor element X (e.g., A1 or B5 or E2, etc.) in a homeowner's PANAS evaluation. P\({}_{\text{x-total}}\) is presented as a positive number. \[\text{P}_{\text{x-total}}=\sum_{i=1}^{10}(\text{P}_{\text{x}}\text{i}) \tag{1}\]  
Step 2: Calculate N\({}_{\text{x-total}}\), which is the sum of negative affects (i.e., N1 + N2\(\ldots\) + N10) expressed by a specific indoor element X (e.g., A1 or B3, etc.) in a homeowner's PANAS evaluation. N\({}_{\text{x-total}}\) is also presented as a positive number. \[\text{N}_{\text{x-total}}=\sum_{i=1}^{10}(\text{N}_{\text{x}}\text{i}) \tag{2}\]  
Step 3: Calculate the V\({}_{\text{x-total}}\), which is the sum of P\({}_{\text{x-total}}\) and N\({}_{\text{x-total}}\) value of this indoor element X. V\({}_{\text{x-total}}\) represents \"the total emotional intensity projected by the homeowner on the indoor element X\", that is, \"the degree to which the homeowner cares about this element X\", and can also be regarded as \"the importance of this element X in the mind of the homeowner\". If the Entropy Weight method is applied for calculation, an item with a wider range of positive and negative information indicates that the information contained in the item is more significant and, therefore, should be assigned a higher weight. \[\text{V}_{\text{x-total}}=\text{P}_{\text{x-total}}+\text{N}_{\text{x-total}} \tag{3}\]  
Step 4: However, in addition to the amount of information about indoor elements (the importance in homeowners' minds), for designers, indoor elements with a high overall negative emotion are the elements that need to be improved first. Therefore, in the design project, the design-weighting of a single element, DW\({}_{\text{x}}\), is defined as \"the importance in the mind of the homeowner, V\({}_{\text{x-total}}\)\" multiplied by the \"overall negative emotion, N\({}_{\text{x-total}}\)\". \[\text{DW}_{\text{x}}=\text{V}_{\text{x-total}}\text{ }^{*}\text{N}_{\text{x-total}} \tag{4}\]  
Step 5: After determining the design weights for the 28 indoor environmental elements, the elements can be sorted based on their weight values. If certain elements exhibit high design weight values and are situated spatially near each other, prioritizing integrated design may be advisable. Consequently, the proportion of budget investment in this specific spatial area can be augmented. After the design-weighting calculation, the indoor elements ranked in the top five by DW\({}_{\text{x}}\) value among the three real projects are shown in Tables 4-6. Consider Project 3 as an illustration. The homeowner in Project 3 is a Feng Shui master, knows how to design the space according to Feng Shui regulations, and frequently entertains guests at his home. By utilizing the design-weighting calculations, enhancements were made to the refinement and illumination of the shrine located in front of the primary column, an area of particular importance to the owner. Subsequently, the outdated concealed ceiling air-conditioning unit was substituted with a robust dual-function heating and cooling system.