Fuzzy arithmetic

N.G. du Bois (n.dubois@wxs.nl)
Wed, 22 Jul 1998 21:01:42 +0200 (MET DST)

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Hello, all interested in fuzzy arithmetic.

I noticed the question about fuzzy arithmetic.

I have a sample of a fuzzy addition using Zadeh's
Extension Principle. I worked it out in a spread sheet.
It is a "Works" program peace of software.
You can change the operation for other simple arithmetic operations,
that is subtraction, multipliing and division. You have to do the change
for each cell that computes, in the spreadsheet. Other operations I did
not work out.
In the first step you define the two fuzzy numbers and the
membershipgrades of their parts.
Second you make the Descartes Product space with the MIN operation
on the membershipgrades (the spreadsheet will do this for you).
Third you work out the operayion cell by cell (in this case an addition)
and you take the outcomes with the highest membershipgrades. (the first
part of this the spreadsheet does itself too.
Then, the selection of the parts of the new fuzzy number with the
highest membershipgrades, this you have to do yourself.

This is a manner to approximate in a very simple but illustrative way
the computation of fuzzy numbers,

Best regards,

Nico du Bois.

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