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Using fuzzy subsets to describe classes imperfectly located in 
,
leads to the characterization of the points of
which are common to different classes or are extraneous to these classes.
The concepts of inclusion, intersection,
union and complement
of fuzzy subsets are thus useful.
As the concept of fuzzy subset is a generalization of the classical
concept of a subset of ,
it is logical to introduce operations on the fuzzy subsets which are equivalent
to the classical operations of set theory (when we deal with membership
functions with values 0 or 1).
Notation In the following paragraphs, 
will represent the set of all the fuzzy subsets of 
.
