Normalized Fuzzy Set,Support Set and Height of Fuzzy Set(English)

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Now you can study the same topic in Hindi at-http://electricalvideolibrary.blogspot.com/2018/09/normalized-fuzzy-setsupport-set-and.html
Today we are going to discuss three things in fuzzy set-
1.Support of Fuzzy Set
2.Height of the Fuzzy Set
3.Normalized Fuzzy Set

Representation of Fuzzy Set:
So Friends before starting the topic lets understand what are the various way in which fuzzy set is represented-

Fig 1.Representation Fuzzy Set

Here the first equation is quite common where we first write the element and then its degree of membership and it can be also represented in the form of addition as you see in the second equation,but beware its just the notation its not actual addition.Similarly we can show it in the form of the summation for discrete data and integration for the continuous  but these are again not the actual summation and integration its just a notation.

Support Set of Fuzzy Set:
Support set is the set of those element whose degree of membership is greater than zero
.Lets see the image for more..

Fig2.Support Set of Fuzzy Set

Here S(A) is the support set of the fuzzy set A.As you can see support set is only having the element not their degree of membership so it is a crisp set or conventional set.


Height of the Fuzzy Set:
Height of the fuzzy set is the maximum value of the degree of membership in the fuzzy set.You can see in the above image for Fuzzy set A the maximum value of degree of membership  is 0.9,so the height of fuzzy set A is 0.9.

H(A)=0.9

Normalized Fuzzy Set:-

Normalized fuzzy set is the fuzzy set whose Height that is maximum of value of degree of membership is 1 if not then it is called non normalized fuzzy set.

Fig 3.Normalized Fuzzy Set

From figure 2 we can see that Fuzzy Set  A mentioned there is non normalized fuzzy set as the height is 0.9.