Rule Simplification Method Based on Covering Indexes for Fuzzy Classifiers

A large number of rules increases the complexity of fuzzy classifiers and reduces the linguistic interpretability of the classification. A tabular rule simplification method that extends the Quine-McCluskey algorithm of Boolean design to fuzzy logic is analyzed in detail in this paper. The method obtains a few compound rules from many initial atomic rules. The influence of membership functions as well as t-norms and s-norms operands, which can be even null if many atomic rules are used, becomes apparent in the classification regions (decision boundaries) induced by the compound rules. Since the compound rules can be ordered according to the covering indexes that measure the number of atomic rules covered, more or less generic classification rules and rules with particular indexes can be further identified, which could ease subsequent classification or decision-making.