L15 fuzzy logic

Fuzzy LogicFuzzy Logic
1Rushdi Shams, Lecturer, Dept of CSE, KUET, Bangladesh

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

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.

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.

An image that describe fuzzy
logic

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".

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

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

Zadeh Operators
 NOT x = (1 - truth(x))
 x AND y = minimum(truth(x), truth(y))
 x OR y = maximum(truth(x), truth(y))

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"

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)

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

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.

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).

Reference
 Wikipedia, “Fuzzy Logic”,
http://en.wikipedia.org/wiki/Fuzzy_logic

L15 fuzzy logic

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