Construction of t-norms

Imagine you have two buckets of pebbles. One is labeled "A" and the other is labeled "B". Now, let's say you want to know how much overlap there is between the pebbles in each bucket.

To figure that out, you can use a special tool called a t-norm. A t-norm helps you compare things and figure out how much they have in common.

The way a t-norm works is a little bit like a scale. You put some pebbles from bucket A on one side of the scale, and some pebbles from bucket B on the other side. Then you weigh them both.

If the pebbles in bucket A weigh more than the pebbles in bucket B, that means there's more overlap between the two buckets. If they weigh the same, then the two buckets have the exact same amount of overlap.

Now, there are different kinds of t-norms that work in different ways. Some are designed to be very strict and only count things that are exactly the same in both buckets. Others are more generous and allow for some differences between the two buckets.

So, depending on what you're trying to measure, you might use a different kind of t-norm. But no matter which one you choose, they all work by comparing two things and figuring out how much they have in common.