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From: jamesw@uhunix.uhcc.Hawaii.Edu (James Williams)
Subject: Re: Membership functions and non-existant data.
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Date: Thu, 27 Apr 1995 15:25:12 GMT
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In article <3nn3ev$kf6@news.ccit.arizona.edu> faf@helium.gas.uug.arizona.edu (Fred A Fox) writes:
>In article <D7JEx7.Ez9@news.hawaii.edu>,
>James Williams <jamesw@uhunix.uhcc.Hawaii.Edu> wrote:
>>Hello again.  Let me try again, perhapse I was a bit fuzzy.
>>
>>Let's start from the real world.  Let's say that I have a set of data,
>>say a profile of biochemical variables measured in the blood.  Let's 
>>say I am implimenting a fuzzy expert system to detect a disorder, i.e.
>>a set of fuzzy rules layered on membership functions. 
>>
>>If the membership functions default to zero when the input to the 
>>membership function is unknown (i.e. the variable was not measured)
>>then the membership function is giving out blarny rather than saying
>>I don't know.  The expert system will then give out blarny.  
>
>(musing deleted)
>
>Why do you default unknown information to zero. This is saying that the
>variable cannot be anything. I would expect that an unmeasured variable
>would have a membership of one everywhere since it was not measured
>and could take on any value. Maybe you could muse some more about how
>this plugs into your rule structure.
>
>
>P.S. Of course you were fuzzy, otherwise you would be doing what you are.
B>

Why default unknown information to zero?  That is exactly my point.  I
asked what a membership function outputs as a response to unknown info.
Someone said it should default to zero.  I don't agree.

Ok a membership function defaulting to 1 for unknown information sounds
good since it would have membership everywhere.  So then:

	high(unknown) = low(unknown) = 1

This may cause a bunch of precepts to be true for unknown information.

	if inocent(unknown) then free(x)
	if guilty(unknown) then hang(x)

	where unknown represents lack of evidence.

Then you have conflicting rules firing simultaneously, you hang a free
man or free a hanged man depending how you want to look at it.  So I think
there are two aspects to truth involved in decisions, the value of a 
measure and the accuracy or the confidance that the measure is true.

Karl Ihrig





