From: gperkins@netcom.com (Glen C. Perkins)
Subject: Re: What does "AND" mean?
Organization: Netcom - Online Communication Services  (408 241-9760 guest) 
Date: Fri, 22 Jan 1993 17:00:05 GMT

pbm@mdis2.wdl.loral.com (Paul Melville) writes:

>In article <1993Jan21.225423.25301@netcom.com> gperkins@netcom.com (Glen C. Perkins) writes:

>>   Suppose I'm looking for a wife "scientifically" (yeah, right) and I 
>>   decide that my rule for evaluating candidates is "the prettier and the 
>>   nicer, the more interested I am." Assume 0.0 PRETTY is elephant 
>>   (wo)man, .5 is average, 1.0 is to die for, and 0.0 NICE is intolerable, 
>>   .5 is average, 1.0 is an angel. If I decide to use MIN to represent AND 
>>   (the most common definition of AND in fuzzy systems), I get:

>   [etc.]

>A thought: You seem to imply that your membership rules for both PRETTY
>and NICE are linear. i.e. if Miss X is "twice" as pretty as Miss Y,
>then,

>	mPRETTY(X) == 2 * mPRETTY(Y)

>what about first choosing a more realistic membership function, one
>that reflects how you feel about the relative importance of that LEVEL
>of PRETTY-ness or NICE-ness.  Like this:

>mNICE(x)^
>     1.0|                                  *****
>        |                          ********
>        |                    ******
>        |                ****
>        |             ***
>     0.5|           **
>        |          *
>        |         *
>        |        *
>        |       *
>     0.0+--------------------------------------->  x
>        0   1   2   3   4   5   6   7   8   9  10
>        ^                   ^                   ^
>        |                   |                   |
>	downright         ave.                angel
>	nasty

>where "x" represents your linear rating of the marital candidate.
>I still think that you are right about wanting soe kind of anD beside
>MIN, but if you calculate membership in the two sets with some kind of
>(easily defined) curve similar to above, then a simple average ight be
>OK, or RMS or whatever.


I'm glad I asked, because this is the kind of suggestion I was
looking for. I actually wasn't using linear membership functions,
but in my consideration of the appropriate rules I was
overlooking the information already encoded in the mem function
and sort of unconsciously assuming something simple and linear.
Using a linear rating system and then running it thru a
PRETTY_ENOUGH and NICE_ENOUGH mem funtion and then ANDing those
makes a LOT more sense. Thanks.

I'm still interested in other good suggestions such as what
AND functions would be most reasonable. This sort of thing has
probably been done somewhere in some form.  When I say "OR"
in conversation, I really do think in terms of a MAX function,
unconsciously of course. At least, I sense that the MAX
function fits my "feeling" of what I mean when I casually
say "or". I'm much less confident of AND, and it doesn't
really matter except when I decide to generate fuzzy rules
to model human psychology (in some narrow domain.)
-- 
+-----------------------+---------------------------------------------------+
|--- Glen C. Perkins ---|                                                   |
| <gperkins@netcom.com> |             "Don't forget, your mind              |
| Native Guide Software |              only *simulates* logic."             |
| Palo Alto, California |                                                   |
+-----------------------+---------------------------------------------------+

Newsgroups: comp.ai.fuzzy