The self-healing characteristic is a key aspect of smart grids and holds important research significance. However, a comprehensive measurement standard for assessing the self-healing ability of smart distribution networks has not yet been established. Existing evaluations of self-healing in smart distribution networks suffer from various issues, such as incomplete quantitative indicators and neglecting uncertainties in the process of self-healing. These problems leads to inaccurate evaluation and higher-than-actual results. To address these challenges, four quantitative indexes, namely, self-healing credibility, self-healing rate, self-healing speed and self-healing benefit are proposed. These indicators encompass factors such as the speed of load recovery, duration of sustainability, and economic benefits following faults in the distribution network. Being built upon these indicators, a comprehensive evaluation metric called “self-repair performance” is proposed using the method of information entropy. Uncertainty theory is introduced to quantitatively describe the uncertainty of self-healing so as to solve the problems of uncertainty and insufficient samples in the evaluation process. A simulation analysis is conducted on a constructed power distribution system with 7 sections to validate the effectiveness and accuracy of the proposed evaluation indexes and method.