AbstractThe problem of sparse fuzzy rule bases is introduced. Because of the high computational complexity of the original compositional rule of inference (CRI) method, it is strongly suggested that the number of rules in a final fuzzy knowledge base is drastically reduced.Various methods of analogical reasoning available in the literature are reviewed. The mapping style interpretation of fuzzy rules leads to the idea of approximating the fuzzy mapping by using classical approximation techniques.Graduality, measurability, and distance in the fuzzy sense are introduced. These notions enable the introduction of the concept of similarity between two fuzzy terms, by their closeness derived from their distance.The fundamental equation of linear ...