On Wed, Mar 11, 2009 at 3:14 PM, Raul Miller <[email protected]> wrote:
> On Wed, Mar 11, 2009 at 1:30 PM, Brian Schott <[email protected]> wrote:
>>        This is sort of a puzzle for which I have a solution
>> but have unsuccessfully puzzled over an alternative solution
>> and wonder if anyone would like to solve the "puzzle" of
>> finding how to find the same result but using I. instead of
>> @. .
>>
>>        My existing solution for the variable trap is as
>> follows.
>
> I am lost here.
>
>> aa =: {...@]
>> dd =: {:@]
>> bb =: 1&{...@]
>> cc =: _2&{...@]
>
> aa bb cc and dd are four points on a trapazoid which is the right arg?
>
> In other words:
>   aa=: 0&{...@]
>   bb=: 1&{...@]
>   cc=: 2&{...@]
>   dd=: 3&{...@]

Yes, you have interpretted aa ... dd correctly.
>
>
>> ls =: leftsupp =:(([-aa)%bb-aa)
>> rs =: rightsupp =:((dd-[)%dd-cc)
>> co =: core =: 1:
>> ns =: nonsupport =: 0:

Fuzzy sets are sets for which a numeric membership in the interval
[0,1] defines the degree to which an element is part of the fuzzy set.
If the elements are the real numbers, say X, then we say that a
membership function defines the degree of membership of each real
number in the fuzzy set of interest.
I will us the following notation to indicate the membership function
of the fuzzy set A: mu_A or mu_A(22)=0.7 states that the membership of
the number 22 in the fuzzy set A is 0.7.
The example might be taken from the more general statement that mu_A: X-->[0,1].

If a fuzzy membership mu_A is defined over the real numbers, say X,
then it is common to refer to all of the real numbers which have mu_A
> 0 as the support of A and all of the real numbers which have mu_A=1
as the core of A.


>
> Presumably ls means left support and rs means right
> support, but what is a support?  What does scaling
> supports by the distance between to points help?
> Also, what's "core" mean?
>
>> ge =:  +/"1@(>:/)
>> le =: 4: - +/&.|."1@(<:/)
>> ag =: ge`2:@. (2: <: ge - le)
>
> ge means greater or equal?  Presumably using
> sum because you have scaled things appropriately
> for your concept of fuzziness?  And le means
> less or equal?  4 seems to come from your
> list of gerunds...
>

The graphic below must be viewed in a nonproportional spaced font.
   ___
  /   \
 /     \
_       _
nllcccrrn    NB. read this row and
sssooosss    NB. this row vertically

Yes, yes, and yes to above guesses.

> Does ag mean  2 <. ge - le?
>
>> trap =: (ns`ls`co`rs`ns) @. ag
>
>>         An example of using trap is as follows.
>>
>>   x:1|:((],:3&+)i. 15) (([,trap)"0 1)/_4]\0 5 10 14 2 6 10 14.5
> ...
>
>>        Notice that all of the outputs of trap are between 0
>> and 1 and they are expressed as proper fractions in the
>> example, but that is only for prettying up the readout here.
>>
>>        If you load 'plot', execute the next line, and watch
>> carefully, you will see why these are  called trapezoids.
>>
>> plot"1 |: ,./;"1/ x:1|:((],:3&+)i. 15) (([,trap)"0 1)/_4]\0 5 10 14 2 6 10 
>> 14.5
>
> I see that you have a range of potential values which I guess essentially
> say "how close is x to the thing on the right".  But I do not know the
> data well enough to even begin to understand this one.
>
> Clarification please?

For example, 0 5 10 14 are the x values that correspond to the four
corners of the first trapezoid. The left support goes from 0 to 5, the
right support goes from 10 to 14 and the core goes from 5 to 10.
Similarly for the second set of four numbers: 2 6 10 14.5 are the four
corners of a second trapezoidal membership function, etc.

>
> Thanks,
>
> --
> Raul

Thank YOU.
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm

Reply via email to