We’ll look into the fuzzy process in more detail shortly but, before you can
begin to understand fuzzy sets, it helps to understand the mathematics of
crisp sets, so our journey into fuzzydom will commence there.
NOTE Interpreting linguistic rules is only one of the many uses of fuzzy logic.
I’ve focused on this application here because it’s one of the most useful features
for game AI programmers. Fuzzy logic has been successfully applied to many
other areas including control engineering, pattern recognition, relational data-
bases, and data analysis. You more than likely have several solid state fuzzy
logic controllers in your home. They might be regulating your central heating
system or stabilizing the image in your video camera.
Crisp Sets
Crisp sets are the mathematical concepts taught in school. They have
clearly defined boundaries: An object (sometimes called an element) either
completely belongs to a set or it doesn’t. This is fine for many problems
since many objects can be precisely classified. After all, a spade is a spade;
it’s not partly a spade and partly a pair of garden shears.
The domain of all elements a set belongs to is called the universe of dis
course. The white rectangle of Figure 10.2 represents the universe of
discourse of integers in the range 1 to 15. The circles inside the UOD
denote the set of even integers and the set of odd integers.
Fuzzy Logic | 417
Crisp Sets
Figure 10.1. Fuzzy rule-based inference
Figure 10.2

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