Commutativity as Prior Knowledge in Fuzzy Modeling ⋆

Abstract. This paper faces with the integration of mathematical properties satisfied by the system as prior knowledge in fuzzy modeling (FM), focusing on the commutativity as a starting point. The underlying idea is to reward the rules in each input fuzzy region that provide good commutativity degrees respecting its complementary —commutatively related— input fuzzy region. With this aim, the similarity between the outputs in both regions will be obtained. The experimental results show the accuracy improvement gained by the proposed method

www.elsevier.com/locate/fss Commutativity as prior knowledge in fuzzy modeling �

In fuzzy modeling (FM), the quantity and quality of the training set is crucial to properly grasp the behavior of the system being modeled. However, the available data are often not large enough or are deficiently distributed along the input space, not revealing the system behavior completely. In such cases, the consideration of any prior knowledge about the system can be decisive for the accuracy achieved by the fuzzy modeling. This paper faces with the integration of mathematical properties satisfied by a system as prior knowledge in FM, focusing on the commutativity property as a starting point. With this aim, several measures are developed to evaluate the commutativity in a fuzzy environment dealing with different elements involved in FM. Then, several approaches are proposed to measure the commutativity degrees of a fuzzy rule with respect to the training set and a simple method is presented to integrate these degrees into the FM task. The experimental results show the accuracy improvement gained by the proposed method. © 2004 Elsevier B.V. All rights reserved