Knowledge-Based Systems

144 Chapter 5 Fuzzy LogiC

Example:

Let A = “ x is bigger than 5” and let B = “x is bigger than 4.” It is easy to see

that A  B is true, because it can never happen that x is bigger than 5 and

not bigger than 4.

5.10 FUZZY INFERENCE

Fuzzy inference provides a powerful framework for reasoning with impre-

cise and uncertain information. The inference procedures are known as gen-

eralized modus ponens (GMP) and generalized modus tollens (GMT).

GMP is described as follows:

Given: X is A, then Y is B

X is A9

One may conclude that Y is B9.

GMT is described as follows:

Given: X is A, then Y is B

Y is B9

One may conclude that X is A9.

Example:

The tomato is very red.

If the tomato is red, then the tomato is ripe.

Then the conclusion can be “the ...