Fuzziness as a recognition problem: using decision tree learning algorithms for inducing fuzzy membership functions

In this article we establish a new method for inducing fuzzy set membership degrees based on empirical training data. The approach is founded on the notion of Redundant Decision Trees (RDT), a generalisation of regular crisp Decision Trees (DT). RDTs suffice in capturing the attribute tests required for recognising crisp concepts, from which the related fuzzy concepts may be unambiguously derived. Potential applications of this method include categorisation and the semiautomatic construction and the statistical evaluation of fuzzy concepts. In addition, since the definition of the membership degrees is effectively based on a robust DT machine learning algorithm, the induced fuzzy membership functions generalise. Thus, with certain assumptions, they output sensible membership degrees of previously unseen objects. In addition to introducing and analysing the basic definitions and algorithms, we briefly evaluate their applicability with examples and present some remarks concerning the scope of the approach.