Post on 19-Jan-2015
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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
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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.
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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.
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An image that describe fuzzy logic
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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".
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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 fanIF temperature IS cold THEN turn down fanIF temperature IS normal THEN maintain levelIF temperature IS hot THEN speed up fan
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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
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Zadeh Operators NOT x = (1 - truth(x)) x AND y = minimum(truth(x), truth(y)) x OR y = maximum(truth(x), truth(y))
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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"
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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)
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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
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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.
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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).
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Reference Wikipedia, “Fuzzy Logic”,
http://en.wikipedia.org/wiki/Fuzzy_logic
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