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Classes of algorithms and their corresponding knowledge representations for the induction of fuzzy logic classification rules include, for example, clustering and fuzzy decision trees. This paper introduces a new class of induction algorithms based on fuzzy set covering principles. We present a set covering framework for concept learning using fuzzy sets, and develop an algorithm, FUZZYBEXA, based on this approach to induce fuzzy classification rules from data. Unlike the induction of fuzzy decision trees that follow a divide-and-conquer strategy, this algorithm performs a separate-and-conquer general-to-specific search of the instance space. We show that the description language allows a partial ordering of candidate hypotheses leading to a lattice of conjunctions to be searched. Properties of the lattice allow the development of new heuristics to guide the search for good concept descriptions and to terminate the search early enough in the induction process. The operation of the algorithm is illustrated and then compared with other well-known crisp and fuzzy machine learning algorithms. The results show that highly accurate and comprehensible rules are induced, and that this methodology is an important new tool in the arsenal of fuzzy machine learning algorithms.