Neural networks and the New Fuzzy Reasoning Method: a fuzzy association patch approach

Fuzzy systems map fuzzy sets to fuzzy sets f:X→Y. The fuzzy Cartesian product A x B defines fuzzy patches in the X × Y input-output space. In the New Fuzzy Reasoning Method (NFRM) the fuzzy patches are weighted and averaged to estimate a desired function f. The subsets of the input universe of discourse and of the output universe of discourse are defined by a domain expert by use of a membership function, m_A(x)→ [0,1]. If these subsets, or fit vectors, do not change with time, the size and location of the fuzzy association patches in input-output space remain constant. The relation matrix R, which weighs each association (A,B) can be manipulated to tune the fuzzy controller. Park et al. (1994) showed that genetic algorithms can be used to tune the fuzzy controller by optimizing the fuzzy relation matrix R. The authors propose a feedforward neural network trained using a gradient descent technique to tune the strength R of each fuzzy patch. Finally, the authors show how the output membership functions can be incorporated into the NN to improve performance of the controller