This paper presents a methodology for implementing adaptive fuzzy systems based on a new concept called virtual fuzzy set. The concept provides a new representation for the consequent part of a fuzzy production rule. A virtual fuzzy set, which consists of two consecutive fuzzy sets with different degrees of membership, is an imaginary fuzzy set located at a location most appropriate for a numerical training sample. The new concept is incorporated into an adaptive algorithm based on the fuzzy rule generation scheme suggested by Wang and Mendel. It is a one-pass build-up procedure and time-consuming iterative training is not required. The proposed method has been applied to the fuzzy modelling of a difficult non-linear system. The results showed that the new algorithm has better performance than the Wang-Mendel approach. The improvement is more significant when the input-output space is quantized with a small number of fuzzy sets.
