Learning fuzzy rules for similarity assessment in case-based reasoning
Expert Systems with Applications: An International Journal
Fuzzy rule-based similarity model enables learning from small case bases
Applied Soft Computing
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The issue of fuzzy systems as universal approximators has drawn significant attention, but all results obtained are restricted to deterministic input-output (I/O) relationships. It should be noted that, in practice, many I/O systems, including fuzzy systems, operate in the environment which is essentially stochastic. In this paper, the Mamdani fuzzy systems are generalized as stochastic systems. By proving the Mamdani systems as universal approximators with L2-norm, the approximation capability of the stochastic Mamdani systems to a class of random processes is systematically analyzed. In the mean square sense, such stochastic fuzzy systems are capable of approximating the prescribed random processes with arbitrary accuracy. Further, an efficient learning algorithm for the stochastic Mamdani systems is developed. Finally, a simulation example is employed to demonstrate our results.