The basics of using floppy sets will be shown in the following applet. Suppose we describe the temperature of water using five primary fuzzy sets:
- Unpleasantly cold
- Pleasantly cold
- Pleasant, neither warm nor cold
- Pleasantly warm
- Unpleasantly warm
In the first graph, we can see the membership functions of these fuzzy sets. When the membership function reaches one, it means that the water of a given temperature definitely has a given property. When zero, it definitely does not have a given property. A more detailed explanation can be found in the applet.
The applet allows us to create floppy sets A and B, which can have meanings such as “The water is warm,” “The water is pleasant,” or “The water is not cold.” Just tick the appropriate boxes.
The applet will also show you how to use conjunction, disjunction, implication, and equivalence. We can model even more complex phrases such as “The water is cold or unpleasant,” or “If the water is warm, then it is pleasant.”
Be sure to click on the informational icons on the page which will point you to what’s important.
Have fun!
Primary fuzzy sets
Setting-up floppy sets
A
B
Pleasantly cold
Unpleasantly cold
Pleasant, neither warm nor cold
Pleasantly warm
Unpleasantly warm
Floppy sets
Intersection and union of floppy sets
Implication and equivalence of floppy sets
Now we can move on to materials about floppy logic.