Re: Algebraic sum

WSiler (wsiler@aol.com)
Sun, 7 Jun 1998 00:28:30 +0200 (MET DST)

The term "algebraic sum" is a buzz word to denote the probabilistic OR, not
actually the sum A+B, and the formula

A OR B = A + B - A*B

is correct. If this operator is used for ORing quantities, the the
corresponding AND operator is the probabilistic AND,

A AND B = A * B

so that the probabilistic OR may be expressed as

A OR B = A + B - (A AND B)

and are valid if the operands are statistically indepedent, that is have zero
correlation.

These formulas have disadvantages in a fuzzy expert system. As the number of
operands increases, their OR tends to increase toward a, and their AND tends to
decrease toward zero, limiting the number of operands which can practically be
used in fuzzy rules.

William Siler

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