# Algebraic sum

N.G. du Bois (n.dubois@wxs.nl)
Sat, 6 Jun 1998 20:31:10 +0200 (MET DST)

This is the first time I send an email to comp ai fuzzy.
I am a physician and very interested in fuzzy logic and its
applications.

I have a question about the algebraic sum.
In literature about fuzzy sets the next formula is often refurred to as
the algebraic sum: A + B - AB.
What we see is an addition minus the algebraic product.
In his original article on fuzzy sets in 1965 in the part about
algebraic operations on fuzzy sets it is stated by Zadeh in another way.
He also calls the algebraic product AB.
But about the algebraic sum he says: " The algebraic sum of A and B is
denoted by A + B and is defined by ƒ(A+B)= ƒA + ƒB, provided the sum
ƒA + ƒB is less or equal to unity". And in note 1 he says: " The dual of
the algebraic product is the sum ....(A'B')' = A + B - AB. ( This was
pointed out by T. Cover)."

So now my question is: which one of them is the algebraic sum?

1. A + B ?

2. A + B - AB ?

And as one of them being the algebraic sum, what is the other sum
called?

Friendly greetings,

Nico du Bois, IJsselstein, Holland.

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