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696 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS--II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 9, SEPTEMBER 1997 Pointer Adaptation and Pruning of MinMax Fuzzy
 

Summary: 696 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS--II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 9, SEPTEMBER 1997
Pointer Adaptation and Pruning of Min­Max Fuzzy
Inference and Estimation
Payman Arabshahi, Member, IEEE, Robert J. Marks, II, Fellow, IEEE, Seho Oh,
Thomas P. Caudell, Member, IEEE, J. J. Choi, and Bong-Gee Song
Abstract--A new technique for adaptation of fuzzy membership
functions in a fuzzy inference system is proposed. The pointer
technique relies upon the isolation of the specific membership
functions that contributed to the final decision, followed by the
updating of these functions' parameters using steepest descent.
The error measure used is thus backpropagated from output
to input, through the min and max operators used during the
inference stage. This occurs 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. Interestingly, the partials of min
and max 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; 1 1 1 ; N]. Then @=@ n = 1 when
n is the maximum and is otherwise zero. We apply this property

  

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

 

Collections: Engineering