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Steepest Descent Adaptation of Min-Max Fuzzy If-Then Rules 1 R.J. Marks II, S. Oh, P. Arabshahi ,

Summary: Steepest Descent Adaptation of Min-Max Fuzzy If-Then Rules 1
R.J. Marks II, S. Oh, P. Arabshahi ,
T.P. Caudell , J.J. Choi , B.G. Song
Dept. of Electrical Engineering Boeing Computer Services
University of Washington FT-10 P.O. Box 24346, MS 7L-22
Seattle, WA 98195 Seattle, WA 98124-0346
Boeing Computer Services
P.O. Box 24346, MS 6C-04
Seattle, WA 98124-0346
A new technique for adaptation of fuzzy membership functions in a fuzzy inference system is proposed. The
technique relies upon the isolation of the specific membership function that contributed to the final decision,
followed by the updating of this function's parameters using steepest descent. The error measure used is thus
back propagated from output to input, through the min and max operators used during the inference stage. This
is feasible because the operations of min and max are continuous differentiable functions and therefore can be
placed in a chain of partial derivatives for steepest descent backpropagation adaptation. More interestingly, the
partials of min and max (or any other order statistic, for that matter) act as `pointers' with the result that only the
function that gave rise to the min or max is adapted; the others are not. To illustrate, let max 1 2 N .
Then n 1 when n is the maximum and is otherwise zero. We apply this property to the fine tuning of
membership functions of fuzzy min-max decision processes and illustrate with an estimation example.


Source: Arabshahi, Payman - Applied Physics Laboratory & Department of Electrical Engineering, University of Washington at Seattle


Collections: Engineering