Paper available: Adaptive fuzzy min-max estimation

[Payman Arabshahi]

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Payman Arabshahi
Jet Propulsion Laboratory               Tel:   (818) 393-6054
4800 Oak Grove Drive                    Fax:   (818) 393-1717
MS 238-343                              Email: payman at jpl.nasa.gov
Pasadena, CA 91109

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TITLE:     Pointer adaptation and pruning of min-max fuzzy inference and
           estimation.
AUTHORS:   Arabshahi-P.  Marks-R-J.  Oh-S.  Caudell-T-P.  Choi-J-J.
SOURCE:    IEEE Transactions on Circuits and Systems II - Analog and 
           Digital Signal Processing.  Vol. 44, no. 9, Sept. 1997, 
           p.696-709.
ABSTRACT:  A new technique for adaptation of fuzzy membership functions in
           a fuzzy inference system is proposed, The painter 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 alpha = max [beta(1),
           beta(2), ..., beta(N)]. Then partial derivative alpha/partial
           derivative beta(n) = 1 when beta(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, The adaptation process
           can reveal the need for reducing the number of membership
           functions, Under the assumption that the inference surface is
           in some sense smooth, the process of adaptation can reveal
           overdetermination of the fuzzy system in two ways, First, if
           two membership functions come sufficiently close to each other,
           they can be fused into a single membership function, Second, if
           a membership function becomes too narrow, it can be deleted, In
           both cases, the number of fuzzy IF-THEN rules is reduced, In
           certain cases, the overall performance of the fuzzy system ran
           be improved by this adaptive pruning.

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