FUZZY SET COVERING AS A NEW PARADIGM FOR THE INDUCTION OF FUZZY CLASSIFICATION RULES

In 1965 Lofti A. Zadeh proposed fuzzy sets as a generalization of crisp (or classic) sets to address the incapability of crisp sets to model uncertainty and vagueness inherent in the real world. Initially, fuzzy sets did not receive a very warm welcome as many academics stood skeptical towards a theory of “imprecise ” mathematics. In the middle to late 1980’s the success of fuzzy controllers brought fuzzy sets into the limelight, and many applications using fuzzy sets started appearing. In the early 1970’s the first machine learning algorithms started appearing. The AQ (for Aq) family of algorithms pioneered by Ryszard S. Michalski is a good example of the family of set covering algo-rithms. This class of learning algorithm induces concept descriptions by a greedy construction of rules that describe (or cover) positive training examples but not negative training examples. The learning process is iterative, and in each iteration one rule is induced and the positive examples covered by the rule removed from the set of positive training examples. Because positive instances are separated from negative instances, the term separate-and-conquer has been used to contrast the learning strategy against decision tree induction that use a divide-and-conquer learning strategy. This dissertation proposes fuzzy set covering as a powerful rule induction strategy. We survey existin