Introduction to Fuzzy Logic, Fuzzy and Crisp Sets
Fuzzy Logic
Fuzzy Logic deals with the degree of truth instead of giving exact true or false as the answer.
For better understanding in simple language, let’s discuss an example here.
There is a pear and there are two sets:
- Set of pears
- Set of pear cores
Now, take a bite of the pear. It will still belong to the set of pears, Right?
Just keep taking the bites and you will reach a point when just a single bite will be left, and after that, the pear will get into the set of pear cores.
Now, the area between both the sets is not clearly defined since the object can not belong to both sets. Now, consider these two sets as fuzzy sets.
Fuzzy Logic Concept
Fuzzy sets provide a degree of membership to each of its member. Take ‘1’ as belonging to the set and ‘0’ as outside the set and object belonging partially to the set will have a degree between 0 to 1.
Hence, when one will take the first bite of pear, then it’s degree of membership will get changed from 1 to 0.9 and furthermore, after another bite it gets converted in 0.8 and then 0.7 and so on up to that 0.1, after which it will no longer belong to the set of pears and will get into the set of pear cores.
The number (from 0 to 1) which is assigned to the object is called the degree of membership.
Fuzzy Sets
In terms of Mathematics, a set is basically a collection of items.
Let’s take an example here:
As the age for giving vote is 18 years, so we have to figure out the people who are eligible for voting and who will be eligible to vote next year for 2019 elections.
For this, the people aged equal or more than 18 will pass the criteria, but people below 18 will not be considered. Even the one with 17 years of age will be marked as ineligible, even though he will be 18 till the next year (coming elections time)
Hence, the fuzzy set comes into play.
It will give a degree of membership as 0.8 to people aged 16 and 0.9 to the people aged 17 years, so that we will get to know that they will be eligible for polling next year.
Crisp Sets
Crisp sets are just like binary sets. It deals with true and false or 0 and 1.
I gives output direct as in or out, there is no in between.
Let’s discuss an example of a race here, according to crisp logic, a threshold will be decided, sat 0.5 and above this person will be considered as fast and below this, slow.
But in fuzzy sets, intermediate values can be discussed as fast, very fast, slow, medium.
Crisp Set VS Fuzzy Set
CRISP SET |
FUZZY SET |
1. Crisp set deals with binary logic. | Fuzzy sets can have intermediate values. |
2. Values here will be exact like 0 or 1 (True or False) | Values can lie between the interval of 0 and 1, like 0.4,0.6 etc. |
3. It deals with boundary values, i.e certain answers. | It’s having a concept of “degree of membership” and thus can deal with uncertain answers. |
4. Example: In a Race: A person can be marked as fast or slow. | Example: Similarly in a Race: Marking can be done on the basis of Slow, Medium, Fast and Very Fast. |