Preference set-based design method for qualitative assessments using dominance-based rough set approach

The preference set-based design (PSD) method enhances design efficiency by providing an adjustment range that reflects the preferences of the designer in the quantitative design variables and performance. However, applying PSD in early design stages, where variables and performance are often qualitative or their relationships fluctuate probabilistically owing to individual differences (probabilistic objective function), is challenging. This study proposes a PSD method that addresses these issues using the rough set theory, which is suitable for handling such design problems. This approach derives if-then rules from data combining qualitative and quantitative design variables and performance. These rules are specified based on four PSD indicators and target either frequently occurring or high-importance data. The proposed method was validated on car evaluation data from a U.S. automobile market. The analysis resulted in decision rules incorporating both quantitative and qualitative design variables, as well as the characteristics of four indicators. This demonstrates the applicability of the proposed method to design problems with qualitative variables and performance or a probabilistic objective function. Additionally, a parameter study of indicator weights yielded diverse decision rules (Pareto optimal solutions) based on the weight ratio, highlighting the ability of the proposed method to generate design solutions aligned with specific characteristics of each indicator, further confirming its applicability to a wide range of design problems.