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Fuzzy Logic
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Example 5: Fuzzy Hedges

Problem. Suppose you had already defined a fuzzy set to describe a hot temperature.

Hot = FuzzyGaussian[20, 7, UniversalSpace 
-> {0, 20}] ;

FuzzyPlot[Hot, PlotJoined -> True] ;

[Graphics:HTMLFiles/hedges_3.gif]

Now, suppose we want to talk about the degree to which something is hot. We need some sort of fuzzy modifier or a hedge to change our fuzzy set. Look at how we can accomplish this.

Solution. We can start by defining how a fuzzy set should be modified to represent the hedges "Very" and "Fairly." Two functions in Fuzzy Logic, Concentrate and Dilate, can be used to define our two hedges.

Very := Concentrate Fairly := Dilate

Now we can look at a graph of the fuzzy sets FairlyHot, Hot, and VeryHot.

FuzzyPlot[Fairly[Hot], Hot, Very[Hot], 
PlotJoined -> True] ;

[Graphics:HTMLFiles/hedges_6.gif]

Note that the FairlyHot membership function is a more general, spread-out fuzzy set. The VeryHot fuzzy set is a more focused, concentrated fuzzy set.

We can also apply more than one modifier to a fuzzy set. For instance, let us compare Hot, VeryHot, and VeryVeryHot.

FuzzyPlot[Hot, Very[Hot], Very[Very[Hot]], 
PlotJoined -> True] ;

[Graphics:HTMLFiles/hedges_8.gif]

As we might expect, the VeryVeryHot fuzzy set is even more concentrated than the VeryHot fuzzy set.

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