A logic-based approach for evaluating interpretability of fuzzy rule-based classifiers

We describe an automatic approach for evaluating interpretability of fuzzy rule-based classifiers. The approach is based on the logical view of fuzzy rules, which are interpreted as rows in truth tables. These truth tables are subject of a minimization procedure based on a variant of the Quine-McCluskey algorithm. The minimized truth tables are used to build new fuzzy rules, which are compared with the original ones in terms of classification accuracy. If the two sets of rules have similar performances, we deduce that the logical view of rules is applicable to the fuzzy classifier, which is hence considered interpretable. On the other hand, a significant difference in classification ability shows that fuzzy rules cannot be interpreted in logical terms, hence linguistic labelling may not be significant. Two illustrative examples show both the cases.