A new approach to fuzzy rule generation: Fuzzy extension matrix

This paper proposes a new approach to fuzzy rule generation from a set of examples with fuzzy representation. The new approach called fuzzy extension matrix incorporates the fuzzy entropy to search for paths and generalizes the concept of crisp extension matrix. By discussing paths of the fuzzy extension matrix, a new heuristic algorithm for generating fuzzy rules is introduced. Compared with the crisp extension matrix, the proposed method has the capability of handling fuzzy representation and tolerating noisy data or missing data. A case study shows that the proposed heuristic algorithm partially inherits the advantages from the crisp case such as simplicity of rules and high learning accuracy. The proposed approach offers a new, practical way to automatically acquire imprecise knowledge.