A Specialization of the k{Nearest Neighbor Classi cation Rule for the Prediction of Dynamical Systems Using FIR

Fuzzy Inductive Reasoning (FIR) is a methodology for qualitative modeling and simulation of systems behavior. FIR inference engine is based on the k-nearest neighbor (k-NN) rule, commonly used in the Pattern Recognition eld. The adaptation of the k-NN in an ad hoc 5-NN method has been proved to be very successful in the past, obtaining good results for diierent kind of systems. However, in some circumstances the prediction is not as good as expected. This paper describes the specialization of the k-NN for the prediction of dynamic systems using FIR, and introduces the concept of Causal Relevancy as an important reenement in the inference engine in order to overcome some deeciencies during the forecast stage. Shannon Entropy measures have been applied to take into account the relative importance of each element in the input vector, a semi{Euclidean distance measure is obtained to found neighbors of a better quality.