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The entire movie antz was computer-generated

Introduction 569


Subset of “”: Sometimes you want to know if one set is wholly contained in another? This is called set inclusion or subset of. Therefore, {1,3} ⊂ B, which reads “the set {1,3} is a subset of B. However, A ⊄ B, which reads “A is not a

subset of B”.

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570 16.

The problem with computers is that they are exact machines and we continually use them to solve inexact or fuzzy problems—or at least try to. In the 1970s, com-puter scientists started applying a technique of mathematics called Fuzzy Logic or Uncertainty Logic to software programming and problem solving. Hence, the fuzzy logic that we are talking about here is really the application of fuzzy set theory and its properties. Therefore, let’s take a look at the fuzzy version of everything we just learned about with standard set theory.

First, when talking about fuzzy set theory, we don’t focus so much on the objects in the set any more. This means that the objects are in the set, but we focus on the degree of membership any particular object has within a certain class. For example, let’s create a fuzzy class or category (see Table 16.1)called “Computer Special FX.”Then, let’s take a few of our favorite movies (mine at least) and estimate how much each of them is in the fuzzy class “Computer Special FX.”

Degree of Membership in Class

100%
20%
75%
50%
90%

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the entire movie antz was computergenerated
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