It's a multi valued logic.
In Boolean logic is two valued logic,where we will say 
an element belongs to a set with memebership 1, if it 
doesnt belogs to the set then it's memebership is 0.

Where as in fuzzy sets we say degree of mebership
between 0 and 1.

For example,we have a set of men's age.
In Boolean logic a person X aged 51 we will say x is old
and a person Y aged 49 we will say young.
In fuzzy logic we say X belongs to the old men set with a 
membership of 0.51 and to youngmen set with a membership of 
0.49

So Boolean logic is our Black&White TV where as Fuzzy logic 
is Colour TV
Fuzzy logic is a Discrete spectrum of values.

fuzzy logic is nothing but the multivalued logic used for 
partially truth statement,where degree of membership is 
encountered whose value ranges from 0 to 1,instead of being 
either 0 or one only

this is implemented in natural language understanding and 
representation where we use linguistic variable like age.