>>> John Boone on Fuzzy Sets 
 WE> Are there biological applications for fuzziness?  
 JB> Yes, many.  I'll begin by using fractals, which IMO, is related 
 JB> to fuzziness.  Fractals are "fuzzy" at the edges.  
I don't think so, yet this is an interesting notion.  Fractals are called 
such as these shapes are not simple 1, 2, or 3 dimensional objects but have 
fractional dimension.  Indeed there's something blurry about these objects.
I'll begin by heart
 JB> rate, HR if one were to plot heart rate as a function of time HR(t), 
 JB> and plot HR(t), y, HR(t-1), x, and assign a "spread fucntion", one 
 JB> finds, such a manipulation is a good predictor of -future- death, 
 JB> in particular myocardial infarctions (I done some research in 
 JB> this area). 
Don't know what you mean HR(t), y, HR(t-1), x.  What's the y and x?  What's a 
spread function?
 JB> Why the big deal?  At present, current technology limits the 
 JB> diagnosis of myocardial infarction by EKG changes which in ...
[Whew, this is too much, like lots of missing background on my part.]
 JB> If -ONE- EKG with a "spread function" determines myocardial 
 JB> infarction, treatment could be started sooner and save 
 JB> significant money. 
So there's lots of room for improvement of diagnosis.
 JB> If one were to look at the structure of circulatory, respiratory, 
 JB> and nervous system, such systems have a fractal nature.   It is 
 JB> proposed, the reason, DNA being the making "code" could generate 
 JB> such diversity, by following a simple -REITERATIVE- "code" 
 JB> (going through the process of transcription and translation) 
 JB> in the language of mathematics, algorithim. 
Indeed, and visa versa, life like formations are generated by such a process.
 JB> For diagnosis, what one does is take the set of {signs} and 
 JB> {symptoms} and assign to a set known as {disease A or not A}. 
 JB> Sets of signs and symptoms are often fuzzy.  For example, 
 JB> the disease caused by "Sarcoptes Scabii" -usually- presents 
 JB> with "severe pruritus".  How does then place what the 
 JB> patient said into or not into, perhaps partly into the 
 JB> set "severe pruritus"; in addition, "minor pruritis" 
 JB> may be "severe pruritis" in another.  
I have a cough or spit phlegm, what's the probability of TB?
I have a cough or spit phlegm, what degree of TB should I assign?
This is a possibility but as I know zilch about fuzzy ...
 JB> I hope this explains, why, I think, fuzzy presents itself 
 JB> in the biological sciences, from the genetic level, to 
 JB> the cellular level and finally to macrosopic level to 
 JB> include the systems and even into the field of medicine. 
I agree about fractals.  I disagree about fractals and fuzzy sets.  It would 
take a decisively new insight to merge the two.  I agree about the last 
example but don't have a glimmer how.  Now if you were to look into the index 
of your books, especially the one on managing uncertainty, for biological or 
medical applications, that would be a start.  Certainly, uncertainty is 
frequent companion to diagnosis.  Let me know if you find any examples.
---
---------------