Membership functions

The slope of a field is considered "gentle" if it is between 0 and 20%, it is considered "average" if it is between 20% and 40% and it is considered "steep" if it is more than 40%.

We say that the slope S of a field may belong to one of three classes:

Class "gentle" if it is measured to be :   

Class "average" if it is measured to be :

Class "steep" if it is measured to be :  

So, the term "belongs to" is `hard'. It means either yes or no.  If the slope of a field is measured to be 19%, it is classified as "gentle". However, instinctively we understand that such a slope is almost "average". The "class system" above does not allow us to express this `almost' we feel about a 19% slope!