newbie question... number of rules, output states

Jason Conolly (conolly@bendnet.com)
Mon, 21 Sep 1998 21:38:15 +0200 (MET DST)

Hi! I am trying to teach myself some fuzzy logic basics for a rule based
control problem. One seemingly obvious question I have not seen answered:
Is there a minimum number of rules necessary?

It seems that given an error signal (e), a velocity signal (delta) fuzzified
into Neg. High, Neg. Low, Zero, Pos.Low, Pos.High then there are 5x5=25
possible states that would require an output rule. However, none of the
examples I have seen include this many rules. Are they simplifying the
rules just to cover the initial state used in the example, or is it common
practice not to define all of the possible states (I suppose, you could
argue that sooner or later most undefined states would deteriorate to
defined states)?

Also, is there some convention that defines the number of states the output
may take? For a NH, NL, ZE, PL, PH system of inputs, it seems like you
could argue a case for some additional states in the output. For example,
given an error of PL and velocity of PL, you could right an output rule of
PL (for the inverted pendulum problem). However, that should indicate an
output rule of less-than PL for e=PL, delta=ZE. Is this accomplished with
hedging or with additional output state definitions? If this is
accomplished with hedging, what is the standard approach to hedging the
output state?

TIA

Please respond to conolly@ieee.org

Jason Conolly, EIT

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