We have discussed only binary
valued logic and classical set theory like :
A person belongs to a set of all
human beings, and if given a specific subset, say all males, then one can say
whether or not the particular person belongs to this set.
This is ok since it is the way
human reason. e.g.,
IF person is male AND a parent
THEN person is a father. The rules are formed using operators.
Here, it is intersection operator
"AND" which manipulates the sets. However, not everything
can be described using binary valued sets.
The grouping of persons into "male"
or "female" is easy, but as "tall" or "not tall" is problematic.
A set of "tall" people is
difficult to define, because there is no distinct cut-off point at which tall
Fuzzy logic was suggested by Zadeh as a method for mimicking the ability of human reasoning using a small number
of rules and still producing a smooth output via a process of interpolation.
Description of Fuzzy Logic
With fuzzy logic an element could
partially belong to a set represented by the set membership. Example, a person of height 1.79 m
would belong to both tall and not tall sets with a particular degree of membership.
Difference between binary logic and fuzzy logic
A fuzzy logic system is one that
has at least one system component that uses fuzzy logic for its internal
Fuzzy system communicate
information using fuzzy sets.
Fuzzy logic is used purely for
internal knowledge representation and externally it can be considered as any
other system component.
Example : Five tumblers
Consider two sets: F and E.
F is set of all tumblers belong to
the class full, and
E is set of all tumblers belong to
the class empty
Definition of the set F and E
The sets F and E have some
elements, having partial membership.
Such kind of non-crisp sets are
called fuzzy sets.
The set "all tumblers"
here is the basis of the fuzzy sets F and E, is called the base set.