This study proposes a harmonic average of support and confidence method (HSC), which is a new way to select important rules from the many rules in the decision tree and thereby build a core rule-based decision tree (CorDT) that more easily explains the insolvency factors related to small and medium-sized enterprises (SMEs) using the HSC. To this end, an insolvency prediction model for SMEs was developed using a decision tree algorithm and technological feasibility assessment data as non-financial datasets. We divided these datasets into three types, a general type, a technology development type and a toll processing type applying characteristics of SMEs. We also applied a cost-sensitive approach and several data balancing techniques to construct the same proportion of healthy and insolvent company samples in the datasets. As a result, the insolvency prediction model applied using the synthetic minority over-sampling technique (SMOTE), an over-sampling technique, showed the highest performance with an average hit ratio of 77.6%. Next, we selected important rules by applying HSC to the decision trees with the highest performance and built CorDTs for three types of SMEs using the selected rules. Finally, using the developed CorDTs, we explained the causes of insolvency by type of SME and presented insolvency prevention strategies customized to the three types of SMEs.