On 01-19-98 William Elliot wrote to John Boone... 
 
        Hello William and thanks for writing, 
  
 WE>  JB> Ok, now take, an "whole apple" but showing some signs of  
 WE>  JB> wear, rot.  Does it belong to the set "whole apple?"  
 
 WE> Nope, it is not whole.  To be pedantic, the short small 
 WE> connecting stem if attached, cannot be broken. -) 
   
  . 
  
 WE>  JB> For example, in smelting, it might take temperature 
 WE>  JB> to be raised "a bit" to increase efficiency.  How much  
 WE>  JB> is "a bit" on the Temperature scale?  
 
 WE> This is a classic application, but alas, I've just glanced 
 WE> at it.  Public library is weak on this topic.  If you have  
 WE> a detailed description of a thermostat control application  
 WE> we could eke out an answer.  That would be an excellent  
 WE> fuzzy start for us. 
    
  No, I don't.  More interesting fuzzy applications include, 
washing machines, cleaners, etc. 
  
 WE>  JB> I see you took my example .  
 
 WE> Racer who jumps the gun is off to a fuzzy start? -) 
   
   Yes . 
  
 WE>  JB> Kosko, makes the point, fuzzy allows us say a glass belongs 
 WE>  JB> to the set "cup" a bit while belong to the set "glass" more.  
 
 WE> Indeed, but ask him to tell you about buckets and leaky 
 WE> cups and how big of a hole my fuzzy bucket may have and if  
 WE> a tube is nearly a bucket with a hole for the bottom and  
 WE> hence a fuzzy cup.  Now consider a tall and narrow bucket  
 WE> with a hole for the bottom, what degree of cup would you  
 WE> assign to a hose? -)  How about the saucer?  How about a  
 WE> flat disk which is a cup with just the bottom remaining?   
 WE> Ask him to assign precise degrees of cuppishness.   
   
  Well, I'll try . 
  
 WE> Language can always outstrip the precise syntactics of 
 WE> mathematics.  Is there something paradoxical about  
 WE> assigning a -precise- degree of whateverness to a fuzzy  
 WE> notion of -somewhat- like the whatever. -) 
 
  Perhaps, it does seem useful, more so than the zero- one 
world. 
 
Take care, 
John 
 
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