Newsgroups: comp.ai.fuzzy
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From: moddy@tovlan.weizmann.ac.il (Teeni Moddy)
Subject: Re: fuzzy state machines?
Message-ID: <1996Dec9.102717.20394@wisipc.weizmann.ac.il>
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References: <32964217.2AE9@uscom.com> <19961205184800.NAA03544@ladder01.news.aol.com> <32A83BF0.267E@metasphere.com>
Date: Mon, 9 Dec 1996 10:27:17 GMT
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Arthur Allen (ada@metasphere.com) wrote:
: wsiler@aol.com wrote:
: > 
: > I'm not sure, but I think that perhaps a Markov chain is an example of a
: > fuzzy state system, since the entries in a Markov matrix are state
: > probabilities. Similarly, if the states are members of a fuzzy set, we can
: > have a system in several states at once to some extent, the grades of
: > membership of the states representing possibilities of that state.
: > 
: > If the number of states increases without limits, we find ourselves into a
: > partial differential equation representing a continuum of states.

: Let us assume that a fuzzy state machine can, as you describe,
: violate the one-state-at-a-time rule and be active in
: multiple states simultaneously, but to varying degrees. 
: Normally, transitions in a Moore Machine are defined by the 
: tuple (from, event, guard, to):  while in state <from> if 
: <event> occurs and <guard> is true, go to state <to>.
: Suppose that one allows fuzzy guards to be employed in lieu 
: of a boolean guard. For example,

: 	event: man[height x] enters room
: 	guard: is tall

: The truth value of the guard is a function of the height of the 
: man that entered. On the occurence of an event (e.g "a man
: enters") transitions enabled by that event (which is crisp, but
: endowed with attributes (e.g. height)) could fire according (?) to the
: degree to which the <from> state is active & the truth value
: of the fuzzy guard. In firing, a transition might conceivably transfer 
: some (?) fraction of the statehood degree of the <from> state to the 
: <to> state.  Suppose we associate a FAM with each
: state. Should the outputs of all FAMs be weighted according to the
: statehood degree of the state to which they belong?

: Does such a formulation (or something better) make sense 
: from an application viewpoint? Is it useful? The state 
: transition computation is certainly a lot more involved 
: that for normal state machines...

Maybe we can model things with that. Let's say a car has 3 states : Slow, 
Fast, and Very fast. The transitions may be:
if you are very fast, and you see a policeman, move to 'fast'
if you are fast and get into a curve, move to 'slow'
if you are slow, and there is no car near  you, move to 'fast'

etc. I think you can use it to simulate traffic.

However, I think it is more intersting in the theoretic viewpoint. What
inputs will make the machine 'stable' in some sort ? How can we tell if
two machines do the same work ? and if we limit ourselves to automata, what
languages are associated with fuzzy automata ( as regular languages are
to traditional automata ), etc.

-Moddy Teeni.
limit ourselves to automata, what can we sa

