Function approximation based on fuzzy rules extracted frompartitioned numerical data

摘要

We present an efficient method for extracting fuzzy rules directlynfrom numerical input-output data for function approximation problems.nFirst, we convert a given function approximation problem into a patternnclassification problem. This is done by dividing the universe ofndiscourse of the output variable into multiple intervals, each regardednas a class, and then by assigning a class to each of the training datanaccording to the desired value of the output variable. Next, wenpartition the data of each class in the input space to achieve a highernaccuracy in approximation of class regions. Partition terminatesnaccording to a given criterion to prevent excessive partition. For classnregion approximation, we discuss two different types of representationsnusing hyperboxes and ellipsoidal regions, respectively. Based on anselected representation, we then extract fuzzy rules from thenapproximated class regions. For a given input datum, we convert, or innother words, defuzzify, the resulting vector of the class membershipndegrees into a single real value. This value represents the final resultnapproximated by the method. We test the presented method on a syntheticnnonlinear function approximation problem and a real-world problem in annapplication to a water purification plant. We also compare the presentednmethod with a method based on neural networks