Machine learning (ML) based systems have been suffering a lack of interpretability. To address this problem, counterfactual explanations (CEs) have been proposed. CEs are unique as they provide workable suggestions to users, in addition to explaining why a certain outcome was predicted. However, the application of CEs has been hindered by two main challenges, namely general user preferences and variable ML systems. User preferences, in particular, tend to be general rather than specific feature values. Additionally, CEs need to be customized to suit the variability of ML models, while also maintaining robustness even when these validation models change. To overcome these challenges, we propose several possible general user preferences that have been validated by user research and map them to the properties of CEs. We also introduce a new method called \uline{T}ree-based \uline{C}onditions \uline{O}ptional \uline{L}inks (T-COL), which has two optional structures and several groups of conditions for generating CEs that can be adapted to general user preferences. Meanwhile, a group of conditions lead T-COL to generate more robust CEs that have higher validity when the ML model is replaced. We compared the properties of CEs generated by T-COL experimentally under different user preferences and demonstrated that T-COL is better suited for accommodating user preferences and variable ML systems compared to baseline methods including Large Language Models.
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