A machine learning framework for fuzzy set covering algorithms

Many machine learning algorithms for concept learning have been developed using description languages based on prepositional logic. In this paper we show how to extend the so-called set covering approach to learn classification rules based on fuzzy sets and fuzzy logic classifications. This increases the expressive power of the learning algorithm for real-valued data, and consequently extends the range of problems that can be addressed using set covering. Since instances belong to fuzzy sets to a certain degree, we design an algorithm that uses the partial ordering of fuzzy sets to construct a fuzzy lattice of concept descriptions. We illustrate the algorithm on a toy example, and present the results of real-world data sets, substantiating the claim that the increased expressive power classifies at least as well and better than comparable crisp learning algorithms.