Overview of Fuzzy Concepts
and Fuzzy Logic Systems
Objectives
• To get an overview of fuzzy systems
• To understand the concept of fuzzy logic
• To learn some applications of fuzzy logic
control (FLC)
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Introduction
• What is Fuzziness?
According to the Oxford English Dictionary,
The word “fuzzy” means blurred, fluffy, frayed or indistinct.
In Malay, fuzzy is “kabur” or “samar” or “kurang jelas”.
• Important points to note
– Fuzziness is deterministic uncertainty
(uncertainty is the lack of exact knowledge that would
enable us to reach a perfectly reliable conclusion)
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Uncertainty in general
“There are some things that you know to be true,
and others that you know to be false; yet, despite this
extensive knowledge that you have, there remain
many things whose truth or falsity is not known to
you. We say that you are uncertain about them. You
are uncertain, to varying degrees, about everything
in the future; much of the past is hidden from you;
and there is a lot of the present about which you do
not have full information. Uncertainty is everywhere
and you cannot escape from it (Dennis Lindley,
Understanding Uncertainty, 2006).”
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• Some important points to note:
– Fuzziness is connected with the degree to which
events occur rather than the likelihood of their
occurrence (probability). For example, the degree to
which a person is young is a fuzzy event rather than a
random event.
– Fuzziness is deterministic uncertainty (uncertainty is
the lack of exact knowledge that would enable us to
reach a perfectly reliable conclusion)
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SOURCES OF UNCERTAINTY
􀂃 Data Measurement
- Errors and Blunders
- Resolution Limits
􀂃 From Random Occurrences
􀂃 Linguistic Imprecision
- Ambiguous
- Imprecise
- Vague
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Example of Linguistic Imprecision
Unusual and Real-Life Quotes
How was the weather like yesterday?
Oh! It was rainy with 98% humidity and hot
with temperature of 35.5 deg C
OR
Oh! It was very humid and really hot.
Which one we normally say?
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How can we represent these expert
knowledge that uses vague and
ambiguous terms in computer? Can
it be done at all?
Through fuzzy logic
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WHAT IS FUZZY LOGIC?
“Fuzzy logic is determined as a set of mathematical principles for
knowledge representation based on degrees of membership rather
than on a crisp membership of classical binary logic (Zadeh, 1965).”
• Unlike two-valued Boolean logic, fuzzy logic is multi-valued.
• Fuzzy logic uses the continuum of logical values between 0
(completely false) and 1 (completely true).
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EXAMPLE 1:
(Example from Artificial Intelligent a Guide to Intelligent Systems by Michael
Negnevitsky)
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Crisp set of ‘tall men’
IS DAVID TALL OR SHORT?
Based on crisp set, David who is 179 cm tall, which is just 2
cm less than Tom, is not tall (or short) man.
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• The basic idea of the fuzzy set theory is that
an element belongs to a fuzzy set with a
certain degree of membership.
• Thus, a proposition is not either true or false,
but may be partly true (or partly false) to any
degree.
• This degree is usually taken as a real number
in the interval [0,1].
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EXAMPLE 1:
(Example from Artificial Intelligent a Guide to Intelligent Systems by Michael
Negnevitsky)
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Fuzzy set of ‘tall men’
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EXAMPLE 2:
(Example from Artificial Intelligent a Guide to Intelligent Systems by Michael
Negnevitsky)
Crisp set of ‘short’, ‘average’ and ‘tall men’
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Fuzzy set of ‘short’, ‘average’ and ‘tall men’
A man who is 184 cm tall is a member of the average men set
with a degree of membership of 0.1, and at the same time, he is
also a member of the tall men set with a degree of 0.4. This
means that a man of 184 cm tall has partial membership in
multiple sets.
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Differences Between
Fuzzy Logic and Crisp Logic
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CRISP
FUZZY
Precise
Properties
Imprecise
Properties
Full Membership
Yes or No
True or False
1 or 0
Partial Membership
Yes --> No
True --> False
1 ---> 0
Crisp Sets
Girls age 13 yrs
People 1.5m tall
Fuzzy Sets
Girls about 13yrs
People about 1.5m tall
Crisp Models
Crisp relations
Fuzzy Models
Fuzzy relations
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Fuzzy Logic Technique
can be applied to ….
 Control Systems
 Decision Support Systems (Diagnostics)
 Pattern Recognition
 Modeling of Systems
 Scheduling Problems
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A Fuzzy Logic Controller
Consists of 4 Elements
1. A rule-base
2. An inference mechanism
3. A fuzzification interface
4. A defuzzification interface
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Why use Fuzzy Logic?
• Fuzzy logic can handle linguistic imprecision
where other techniques have difficulty in
handling.
• Fuzzy logic is conceptually easy to understand.
The mathematical concepts behind fuzzy
reasoning are very simple. What makes fuzzy nice
is the “naturalness” of its approach.
• Fuzzy logic is flexible.
With any given system, it’s easy to massage it or
layer more functionality on top of it without
starting again from scratch.
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Why use Fuzzy Logic?
• Fuzzy logic can be built on top of the experience of
experts.
In direct contrast to neural networks, which take
training data and generate opaque, impenetrable
models, fuzzy logic lets you rely on the experience of
people who already understand your system.
• Fuzzy logic can be blended with conventional
control techniques.
Fuzzy systems don’t necessarily replace conventional
control methods. In many cases fuzzy systems
augment them and simplify their implementation.
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Brief History of Fuzzy Logic
• 1965 - Seminal Paper by Prof. Lotfi Zadeh on Fuzzy Sets
• 1966 - Fuzzy Logic (P.Marinos, Bell Labs)
• 1972 - Fuzzy Measure (M. Sugeno, TIT)
• 1974 - Fuzzy Logic Control (E.H. Mamdani, London Q. Mary)
• 1980 - Control of Cement Kiln (F.L. Smidt, Denmark)
• 1987 - Sendai Subway Train Experiment, Japan (Hitachi)
• 1988 - Stock Trading Expert System (Yamaichi Securities)
• 1989 - LIFE (Lab for International Fuzzy Eng.)
Japanese Govt. provides US$70million on Fuzzy research
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Brief History of Fuzzy Logic (cont.)
• 1989 - First Fuzzy Logic Air-Conditioner
• 1990 - First Fuzzy Logic Washing Machine
• 1990~1994 - Japanese Companies
develops Fuzzy Logic application in a big way
• 1994 - Japanese companies sold over US$34billion of fuzzy
logic consumer products
• 1992 ~ 1998 - Research on neuro-fuzzy techniques
• 2000 - ?
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Fuzzy sets were introduced by Lotfi Zadeh in 1965 to represent
and/or manipulate data and information possessing nonstatistical
uncertainties.
L.A.Zadeh, Fuzzy
Sets, Information and
Control, 8(1965) 338353.
It was specifically designed to mathematically represent uncertainty
and vagueness and to provide formalized tools for dealing with the
imprecision intrinsic to many problems.
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The Success of Fuzzy Logic is mainly due
its introduction into Consumer Products
Early Applications started in Japan since 1980s, some
examples are:
 Sendai Subway System
 Temperature Controller in Showers
 Air Conditioner
Tokyo’s Electric Town - Akihabara
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The Revolution of the
Consumer Products
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In 1990, with the introduction of Fuzzy Logic Washing
Machines, extremely high sales were recorded!
This prompted many other consumer product manufacturers
to start using fuzzy logic in their products.
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Example of fuzzy rules in washing
machines
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With an advanced microprocessor, the fuzzy logic rice
cooker can steam, slow cook and with functions for
preparing brown rice as well as porridge.
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Fuzzy Logic Automatic
Gear Shift Control in Vehicles
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Fuzzy Logic Automatic Gear
Shift Control
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Summary
• It can handle imprecision and uncertainty of the real
world.
• It has been successfully applied into many commercial
products.
• Fuzzy techniques can be incorporated into many
products/systems for better performance.
• A number of fuzzy logic systems have been designed in
Malaysia.
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