Re: Fuzzy calc question

savinov@usa.net
Sun, 21 Jun 1998 17:06:25 +0200 (MET DST)

In article <6mbhhv$r6h$1@news.monmouth.com>,
"John" <blackdog72@netlabs.net> wrote:
>
> I just downloaded a fuzzy calculator.
> Can anyone explain to me why .5 plus .5 equals .75?
> Thanks
>

If you downloaded it from my home page
http://www.geocities.com/ResearchTriangle/7220/
then I can answer.

This toy program simulates an ordinary calculator but
uses ordinary real numbers from the interval [0,1] and
T-norm and conorm as operations (i.e., it does not use
fuzzy distributions as numbers like all other calculators).

The operation of multiplication is defined as follows:

i(x,y) = log_s [1 + (s^x-1)(s^y-1)/(s-1)]

where s is a parameter of the operation (set in the About
dialog -- default value is 1). There are also other formulas
but in our calculator we implemented this one.

In particular,
- if s = 0, i(x,y) = min(x,y)
- if s = 1, i(x,y) = xy
- if s = infinity, i(x,y) = max(0,x+y-1)

The sum is defined from the condition:
u(x,y) + i(x,y) = x + y

In particular,
- if s = 0, u(x,y) = max(x,y)
- if s = 1, u(x,y) = x + y - xy
- if s = infinity, u(x,y) = min(1,x+y)

If you used default parameter s=1, then

0.5 + 0.5 = u(0.5,0.5) = 0.5 + 0.5 - 0.5*0.5 =
= 1 - 0.25 = 0.75

Regards,

--
Alexandr A. Savinov, PhD
Senior Scientific Collaborator, Laboratory of AI Systems
Inst. Math., Moldavian Acad. Sci.
str. Academiei 5,  MD-2028 Kishinev, Moldavia
Tel: +3732-73-81-30, Fax: +3732-73-80-27
E-mail: savinov@math.md
URL: http://www.geocities.com/ResearchTriangle/7220/

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