Learning fuzzy relational descriptions using the logical framework and rough set theory

Handling numerical features is quite an open problem for the symbolic approach to machine learning. Indeed, many systems have a limited applicability because of their impossibility to deal with numerical data. In this paper, we propose an approach for learning definitions of concepts from their examples, in the presence of numerical but also uncertain data. This approach fits in a First Order Logic framework and its main characteristics are: (1) the use of fuzzy sets to represent numerical data and model uncertain features, and (2) an inductive learning process based on Rough Set Theory which is capable of handling uncertainty within the learning data. Compared to classical symbolic approaches to inductive learning, it differs in two main points: firstly, it becomes possible to represent both sharp and flexible concepts, and secondly the definitions of concepts that are learned are not deterministic but fuzzy. This approach has been implemented through the EAGLE system and evaluated on a real-world problem of organic chemistry. The results obtained show its good potentialities.