Interpolation, Completion, and Learning Fuzzy Rules

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Fuzzy inference systems and neural networks both provide mathematical systems for approximating continuous real-valued functions. Historically, fuzzy rule bases have been constructed by knowledge acquisition from experts while the weights on neural nets have been learned from data. This paper examines algorithms for constructing fuzzy rules from input-output training data. The antecedents of the rules are determined by a fuzzy decomposition of the input domains. The decomposition localizes the learning process, restricting the influence of each training example to a single rule. Fuzzy learning proceeds by determining entries in a fuzzy associative memory using the degree to which the training data matches the rule antecedents. After the training set has been processed, similarity to existing rules and interpolation are used to complete the rule base. Unlike the neural network algorithms, fuzzy learning algorithms require only a single pass through the training set. This produces a computationally efficient method of learning. The effectiveness of the fuzzy learning algorithms is compared with that of a feedforward neural network trained with back-propagation.