Example 5: Fuzzy Hedges

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

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.

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

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.

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