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From: dfuess@netcom.com (David A. Fuess)
Subject: Re: Membership functions and non-existant data.
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Date: Sun, 30 Apr 1995 14:51:45 GMT
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In article <RBREWER.95Apr29173036@rwb114.rh.psu.edu>
rbrewer@psu.edu <rbrewer@psu.edu> wrote:
> I still don't quite follow you.  Let me extend your cholesterol
> example, and see what we can come up with.
> 
> Maybe some of your rules dealing with diagnosis look as follows:
> 
> IF Cholesterol HIGH and OtherTests LOW then
>       Disease_X_is_present
> 
> IF Cholesterol LOW and OtherTests LOW then
>      Disease_Y_is_present
> 
> IF Cholesterol HIGH and OtherTests HIGH then
>     Disease_Z_is_present
> 
> IF Cholesterol LOW and OtherTests LOW then
>     Healthy_Patient
> 
> Just as examples.  Now, when you run a set of tests, usually the
> result for Cholesterol is somewhere in the HIGH set or the LOW set,
> and maybe in both sets if they overlap.  However, if the test is not
> performed, then the result should be in neither HIGH nor LOW.  Then
> (using max-min composition) none of the rules listed above would
> "fire", and your final diagnosis would be based on the output of
> other rules in the system.
> 
> So could you represent the results of a cholesterol test not performed
> as a number not in the domain of any of the cholesterol fuzzy sets?
> 
> -Rob

Take a closer look at the expected performance of the rules. If data are not 
present for any of the rule inputs (i.e. you simply do not know and cannot 
infer...), the rule should not fire. In the above case, if Cholesterol is 
unknown then no diagnosis involving cholesterol should be performed. One way 
to assure that the rule does not fire is to have the membership function 
return sero. To return 1 implies that the patient has all cholesterol levels 
at the same time which evaluates to the presence of Disease_X, Disease_Y, and 
good health at the same time when the output should be that no inference can 
be drawn on the basis of unknown cholesterol data, hence, none of the stated 
rules should fire.
