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“Generating Fuzzy Rules from Numerical Data, with Applications”
by Li-Xin Wang and Jerry M. Mendel
January 1991
In this report, a general method is developed to generate fuzzy rules from numerical data. This new method consists of five steps: Step 1 divides the input and output spaces of the given numerical data into fuzzy regions; Step 2 generates fuzzy rules from the given data; Step 3 assigns a degree to each of the generated rules for the purpose of resolving conflicts among the generated rules; Step 4 creates a combined Fuzzy-Associative-Memory (FAM) Bank based on both the generated rules and linguistic rules of human experts; and, Step 5 determines a mapping from input space to output space based on the combined FAM Bank using a defuzzifying procedure. The mapping is proved to be capable of approximating any non-linear function on a compact set to arbitrary accuracy. Applications to truck backer-upper control [1] and time series prediction [2] problems are presented. For the truck control problem, the performance of this new method is compared with a neural network controller and a pure limited-rule fuzzy controller; the new method show the best performance. For the time series prediction problem, results are compared by using the new method, a neural network predictor, and a AR model predictor for real time series data and a chaotic time series.