2. Introduction
Form of multivalued logic
Deals reasoning that is approximate rather
than precise
the fuzzy logic variables may have
a membership value of not only 0 or 1 –
that is, the degree of truth of
a statement can range between 0 and 1 and
is not constrained to the two truth values of
classic propositional logic
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 2
3. Introduction
Fuzzy logic has been applied to many fields,
from control theory to artificial intelligence
it still remains controversial among
most statisticians, who prefer Bayesian
logic, and
some control engineers, who prefer
traditional two-valued logic.
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 3
4. Degrees of truth
let a 100 ml glass contain 30 ml of water.
Then we may consider two concepts: Empty
and Full.
The meaning of each of them can be
represented by a certain fuzzy set.
Then one might define the glass as being
0.7 empty and 0.3 full.
The concept of emptiness would
be subjective and thus would depend on
the observer or designer.
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 4
5. An image that describe fuzzy
logic
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 5
6. An image that describe fuzzy
logic
A point on that scale has three "truth
values" — one for each of the three
functions.
Since the red arrow points to zero, this
temperature may be interpreted as "not
hot".
The orange arrow (pointing at 0.2) may
describe it as "slightly warm" and
the blue arrow (pointing at 0.8) "fairly cold".
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 6
7. Fuzzy Rules
fuzzy logic usually uses IF-THEN rules
Rules are usually expressed in the form:
IF variable IS property THEN action
For example, a simple temperature
regulator that uses a fan might look like
this:
IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain level
IF temperature IS hot THEN speed up fan
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 7
8. Fuzzy Rules
There is no "ELSE" – all of the rules are
evaluated, because the temperature might
be "cold" and "normal" at the same time to
different degrees.
The AND, OR, and
NOT operators of boolean logic exist in
fuzzy logic, usually defined as the minimum,
maximum, and complement
when they are defined this way, they are
called the Zadeh operators
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 8
9. Zadeh Operators
NOT x = (1 - truth(x))
x AND y = minimum(truth(x), truth(y))
x OR y = maximum(truth(x), truth(y))
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 9
10. Hedges
There are also other operators, more
linguistic in nature, called hedges that can
be applied.
These are generally adverbs such as "very",
or "somewhat"
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 10
11. Fuzzy Logic Applications
Air conditioning
Washing Machines (LG is the pioneer)
Mono-rails (first used in Tokyo)
Digital image processing (specially in medical imaging)
Elevators (in case of power failure)
Rice cookers
Video game engines (disperse intelligence in prince of
Persia)
Special effects (swarm intelligence in Batman Begins,
Terminator Salvation, The Lord of the Rings)
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 11
12. Objections against Fuzzy Logic
The concept of "coldness" cannot be
expressed in an equation, because although
temperature is a quantity, "coldness" is not
people have an idea of what "cold" is, and
agree that there is no sharp cutoff between
"cold" and "not cold"
where something is "cold" at N degrees but
"not cold" at N+1 degrees — a concept
classical logic cannot easily handle
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 12
13. Objections against Fuzzy Logic
The result has no set answer so it is
believed to be a 'fuzzy' answer.
Fuzzy logic simply provides a mathematical
model of the vagueness which is manifested
in the above example.
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 13
14. A new way to represent
probabilistic logic?
fuzzy set theory uses the concept of fuzzy
set membership (i.e., how much a variable
is in a set)
probability theory uses the concept
of subjective probability (i.e., how
probable do I think that a variable is in a
set).
Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh 14
