What is µ A below ~ x in the Fuzzy Logic I am reading the book "Fuzzy Logic with Engineering" written by Timothy J. Ross and there is a phrase in the book at page 90, he mentions about the "Features of the Membership Function". He says:


  The support of a membership function for some fuzzy set A under ~ is
  defined as that region of the universe that is characterized by
  nonzero membership in the set A under ~. That is, the support
  comprises  those elements x of the universe such that μ A under ~
  (x)>0.


He denotes it as a graphical representation: 



what is μ A under ~ (x) in this context?  Thanks in advance.

Edit Post
The μ A under ~ (x) in this context is membership function. https://www.tutorialspoint.com/fuzzy_logic/fuzzy_logic_membership_function.htm
Here μ A˜(∙) μA~(∙) membership function of A˜ this assumes values in the range from 0 to 1, i.e.,  μ A ˜ (∙)∈[0,1] μA~(∙)∈[0,1] . The membership function  μ A ˜ 
(∙)  μA~(∙) maps   U to the membership space M . The dot  (∙) in the membership function described above, represents the element in a fuzzy set; whether it is discrete or continuous. 

In classical set theory, it is either 1 or 0. 

source:

https://www.tutorialspoint.com/fuzzy_logic/fuzzy_logic_membership_function.htm