Re: Fuzzy arithmetic calculator

Good questions. My answer are along the way, after each question.

Borked Pseudo Mailed wrote:

1. What I use a fuzzy calculator for? Do you have
a practical example?

The use of a calculator is related to arithmetic In agreement with and
quoting from
http://education.yahoo.com/reference/dictionary/entry/arithmetic , I
would define arithmetic s "The mathematics of integers, rational
numbers, real numbers, or complex numbers under addition, subtraction,
multiplication, and division.". When we speak about a fuzzy
calculator, we can say that fuzzy arithmeticsis "The mathematics of
fuzzy integers, fuzzy rational numbers, fuzzy real numbers, or fuzzy
complex numbers under addition, subtraction, multiplication, and
division.".

As a good reference about fuzzy arithmetic, I would suggest:
Arnold Kaufmann, Madan M. Gupta, "Introduction to fuzzy arithmetic
- Theory and Applications", 1985 Van Nostrand Reinhold Company Inc,
ISBN: 0-442-23007-9

The authors have written also another book where there are some nice
examples:
Arnold Kaufmann, Madan M. Gupta, "Fuzzy mathematical models in
engineering and management science", North Holland, ISBN: 044470501 5
In particular, they show examples of the "fuzzy Delphi method",
"discounting problem using fuzzy numbers", and "critical path
method with fuzzy data".

Another book with examples of fuzzy arithmetic is:
George Bojadziev, Maria Bojadziev, "Fuzzy logic for business,
finance, and management", 1997 World Scientific Publishing Co., ISBN:
9810228945

2. Is there some web page with links to fuzzy
calculators?

I do not know, but, probably, substitute for trying:
http://www.google.com/search?hl=en&q=fuzzy+calculator&btnG=Search&meta=

or equivalent string.

3. What are the performance evaluation criteria for
Fuzzy calculators? What makes one good
and the other one bad?

This is more difficult, because it subjective. Nico du Bois, active
member of comp.ai.fuzzy, has developed a fuzzy calculator that can be
found at http://home.planet.nl/~n.dubois/FzCalc/Fcalc.htm . Actually,
the entire http://home.planet.nl/~n.dubois/ is very interesting.
It is a good starting point, but it does not plot the fuzzy numbers. It
would have been harder to do, but it would have been more immediate (a
picture is worth a 1000 words).
In short, I would say that a good fuzzy calculator has the same
characteristics of a good non-fuzzy calculator plus the following
additional functionality:
- ability to define different shapes for a fuzzy number;
- ability to display graphically every fuzzy number and every fuzzy
intermediate result
- has a virtual "paper tape" (you can read what you typed).
4. Did you develop a fuzzy calculator? Do you
have a link? Is the source public domain?
Why did you do it? How long did it take?

No.

Dmitry A. Kazakov, http://www.dmitry-kazakov.de, has good stuff for
anybody wanting to code a fuzzy calculator (
http://www.dmitry-kazakov.de/ada/fuzzy.htm ).

By the way, anybody who has done one, is living within driving distance
from the University of Toronto, and is willing to give a talk about
his/her fuzzy calculator to the local CIS chapter of the IEEE, should
write to me. I am the chapter chair (
http://toronto.ieee.ca/chapters/s_ci.htm ).

5. What are the learning outcomes to be achieved
by doing one's own fuzzy calculator? Is it
time well spent? (I mean intellectually; I have
a steady job, not very demanding intellectually,
that pays my bills and comes with good benefits;
I have an after hours math hobby).

Once you have done it well and once you have posted it to the public
domain, thus opening yourself to criticism and improvement, and once
you have made good use of that criticism, you will have learnt well
fuzzy arithmetic and software product development.

If I decide to develop one, I need to decide how.
I understand fuzzy arithmetic. I tried to do fuzzy
arithmetic by "manual construction" (point by point).
I get good results, repeatable and consistent with
books. I am not so good with software. I can do
simple programs in C and C++, but I am really lousy
with GUIs. Learning how to do GUIs under MS
Windows is not how I really want to invest my time.
Is there any easy to use application that I can
use to display my results?
Start with a good "use case analysis"and a good design spec. The
rest is all a consequence of these two activities. If you publish your
use case analysis and your design spec, some of us will provide you
with feedback and you will improve your product.

Good luck

Best regards


Bruno Di Stefano

--
-- Bruno Di Stefano
----------------------------------------------------------
Bus.: nuptek@xxxxxxxxxxxx www3.sympatico.ca/nuptek
Bruno.DiStefano@xxxxxxxxx http://bruno.distefano.googlepages.com/home
IEEE: b.distefano@xxxxxxxx

PS
==
I will repost this message to the Google Fuzzy Logic Newsgroup. It is a
moderated newsgroup. I feel that we could have a more vibrant virtual
community if we were all posting and responding there. There are few
posters, but they are all serious professionals and dedicated
enthusiasts.

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Borked Pseudo Mailed wrote:
Doing some google searches I just found out about
fuzzy calculators or fuzzy arithmetic calculators.
However, I have some questions that I do not seem
to be able to answer just by doing searches.

1. What I use a fuzzy calculator for? Do you have
a practical example?
2. Is there some web page with links to fuzzy
calculators?
3. What are the performance evaluation criteria for
Fuzzy calculators? What makes one good
and the other one bad?
4. Did you develop a fuzzy calculator? Do you
have a link? Is the source public domain?
Why did you do it? How long did it take?
5. What are the learning outcomes to be achieved
by doing one's own fuzzy calculator? Is it
time well spent? (I mean intellectually; I have
a steady job, not very demanding intellectually,
that pays my bills and comes with good benefits;
I have an after hours math hobby).

If I decide to develop one, I need to decide how.
I understand fuzzy arithmetic. I tried to do fuzzy
arithmetic by "manual construction" (point by point).
I get good results, repeatable and consistent with
books. I am not so good with software. I can do
simple programs in C and C++, but I am really lousy
with GUIs. Learning how to do GUIs under MS
Windows is not how I really want to invest my time.
Is there any easy to use application that I can
use to display my results?

Thank you very much for whatever help I can get.
I really have no friends I can talk with. I work
in an environment where the main interests are
alcohol, sport (watching not practicing), and porno
(again watching, not practicing). I have no friends
or colleagues with my hobbies. I live far from any
college or university. I can nurture my hobbies only
via internet. Thank you again.

Sean

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Dmitry A. Kazakov wrote:
On Wed, 28 Jun 2006 13:27:01 -0600 (MDT), Borked Pseudo Mailed wrote:

1. What I use a fuzzy calculator for? Do you have
a practical example?
2. Is there some web page with links to fuzzy
calculators?
3. What are the performance evaluation criteria for
Fuzzy calculators? What makes one good
and the other one bad?
4. Did you develop a fuzzy calculator? Do you
have a link? Is the source public domain?
Why did you do it? How long did it take?
5. What are the learning outcomes to be achieved
by doing one's own fuzzy calculator? Is it
time well spent? (I mean intellectually; I have
a steady job, not very demanding intellectually,
that pays my bills and comes with good benefits;
I have an after hours math hobby).

AFAIK, Nico du Bois wrote one.

If I decide to develop one, I need to decide how.

Well, no. You start with the requirements. 'How' is about an implementation
of those.

I understand fuzzy arithmetic. I tried to do fuzzy
arithmetic by ´manual construction¡ (point by point).

Do you mean fuzzy numbers? Linguistic variables? General fuzzy sets?

I get good results, repeatable and consistent with
books. I am not so good with software. I can do
simple programs in C and C++, but I am really lousy
with GUIs.

OK, see above. Requirements first: should it be platform-independent?
Graphical / console (scripting)? An embeddable / pluggable component (as a
widget or applet) etc. Language choice is secondary to requirements.

GUI developing is boring, but simple. You would probably have much more
problems with writing a compiler, if you choose to allow expressions and
named variables in your calculator.

[ I have an implementation of fuzzy numbers, and an almost ready compiler
(from FCL). Some GTK widgets for fuzzy sets/linguistic variables are
implemented / planned, but I don't know when I will be ready.]

--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////

--
-- Bruno Di Stefano
----------------------------------------------------------
Bus.: nuptek@xxxxxxxxxxxx www3.sympatico.ca/nuptek
Bruno.DiStefano@xxxxxxxxx http://bruno.distefano.googlepages.com/home
IEEE: b.distefano@xxxxxxxx

/////////////////////////////////////////////////////////////////////////////////////////////////////////////////

.

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