Fuzzy Inductive Logic Programming: Learning Fuzzy Rules with their Implication

Inductive logic programming (ILP) is a generic tool aiming at learning rules from relational databases. Introducing fuzzy sets arid fuzzy implication connectives in this framework allows us to increase the expressive power of the induced rules while keeping the readability of the rules. Moreover, fuzzy sets facilitate the handling of numerical attributes by avoiding crisp and arbitrary transitions between classes. In this paper, the meaning of a fuzzy rule is encoded by its implication operator, which is to be determined in the learning process. An algorithm is proposed for inducing first order rules having fuzzy predicates, together with the most appropriate implication operator. The benefits of introducing fuzzy logic in ILP and the validation process of what has been learnt are discussed and illustrated on a benchmark.