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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:

enter image description here

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

tahasozgen
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1 Answers1

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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

tahasozgen
  • 143
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