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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: Mon, 24 Apr 1995 11:36:43 GMT
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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.  

It seems to me that the membership function should have another dimension.
That is how sure it is.  (People with a little experience with prolog
functions know that the return value is either yes or no depending on
if there was enough information input to come up with an answer.)  I am
thinking along the lines of Kosko's fuzzy hypercube described in Chapter
"American Samurai" in McNeil and Freiberger's *Fuzzy Logic: the 
revolutionary computer technology that is changing our world*.  So in the
fuzzy hypercube there would be an axis which represented "sureness", 
"confidance" or "certainty".  

So, back to the non-available data input into the membershipf function.
The membership function might output two values, the membership and the
"confidance" of the membership.  Where the range of confidance is between
1 and 0.  So given no input, the membership function would output a 
default membership value with a "confidance" of 0 (sholder shrug).  The
"confidance" values would then just be shoved through the AND (MIN) and 
OR (MAX) precepts to give "certainty" of the membership in the precept.  

In real life we are not equally "sure" or "certain" about every precept.
Some are half baked, others are stronger.

Another consideration might be to have membership functions recieve and
give fuzzy numbers.  (I'll have to think about this one a bit.)

Hope this is clearer than my last posting.  Any comments?

------------------------------------------------------------
Karl Enrique Ihrig	ihrig@v1.eph.qub.ac.uk (Belfast)


 


