1. No category

Fuzzy Logic,
i Sets
S andd Systems
S
Lecture 1
Introduction
Hamidreza Rashidy Kanan
Assistant Professor,
Professor Ph
Ph.D.
D
Electrical Engineering Department, Bu-Ali Sina University
h.rashidykanan@basu.ac.ir; kanan_hr@yahoo.com
Fuzzy Logic, Sets and Systems
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Fuzzy Logic, Sets and Systems
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Course Information
 Evaluation Policy
Final Exam 70%
 Project 30%
 Text/Reference Books
[1] Li Xin Wang, “A course in fuzzy systems and control”,
Prentice Hall 1997.
Prentice-Hall,
1997
[ ] Timothy
[2]
y J. Ross,, “Fuzzy
y Logic
g with Engineering
g
g
Applications”,John Wiley & Sons, 2004.
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Course Information
 Objective
To provide a basic understanding of the:
 Fuzzy Logic, Sets and their mathematics.
 Design methods of Fuzzy systems.
 Some applications of Fuzzy systems.
 Pre-requisites
Calculus and MATLAB Software.
Fuzzy Logic, Sets and Systems
Syllabus
5
 Introduction
 The Mathematics of Fuzzy Systems
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Fuzzy Sets and Basic Operations on Fuzzy Sets
Further Operations on Fuzzy Sets
Fuzzy Relations and the Extension Principle
Linguistic Variables and Fuzzy IF-THEN Rules
Fuzzy Logic and Approximate Reasoning
 Fuzzy Systems and Their Properties
 Fuzzy
F
R
Rule
l Base
B
andd Fuzzy
F
IInference
f
E
Engine
i
 Fuzzifiers and Defuzzifiers
Fuzzy Logic, Sets and Systems
Syllabus
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 Fuzzy Systems as Nonlinear Mappings
 Approximation Properties of Fuzzy Systems (I)
 Approximation Properties of Fuzzy Systems (II)
 Design of Fuzzy Systems from Input-Output Data
 Design of Fuzzy Systems Using A Table Look-Up Scheme
 Design of Fuzzy Systems Using Gradient Descent Training
 Fuzzyy Classification and Clustering
g
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Professional Organizations and Networks
International Fuzzy Systems Association (IFSA)
Japan Society for Fuzzy Theory and Systems (SOFT)
Berkeley Initiative in Soft Computing (BISC)
Northh A
American
i
Fuzzy Information
f
i Processing
i Society
S i (NAFIPS)
( A S)
Spanish Association of Fuzzy Logic and Technologies
Th European
The
E
Society
S i t for
f Fuzzy
F
Logic
L i andd Technology
T h l
(EUSFLAT)
EUROFUSE
Hungarian Fuzzy Society
EUNITE
Fuzzy Logic, Sets and Systems
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Fuzzy Logic Journals
Journal of Fuzzy Sets and Systems
The Journal of Fuzzy Mathematics
International Journal Uncertainty, Fuzziness and Knowledge-Based Systems
IEEE Transactions on Fuzzy Systems
International Journal of Approximate Reasoning
Information Sciences
International Journal of Intelligent Systems
M th
Mathware
and
dS
Soft
ft Computing
C
ti
Journal of Advanced Computational Intelligence & Intelligent Informatics
Journal of Intelligent & Fuzzy Systems
Soft Computing
Electronic Transactions on Artificial Intelligence (ETAI)
Biological Cybernetics
International Journal of Computational Intelligence and Applications (IJCIA)
International Journal of Intelligent Control and Systems (IJICS)
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Main Components of an Expert System
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Main Components of an Expert System
 Knowledge Base
 Contains essential information about the problem domain
p
as facts and rules
 Often represented
 Inference Engine
 Mechanism to derive new knowledge from the knowledge
base and the information provided by the User
 Often based on the use of rules
 User Interface
 Interaction with
ith end users
sers
 Development and maintenance of the knowledge base
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Wh F
Why
Fuzzy
 Based on intuition and judgment
 No need for a mathematical model
 Provides a smooth transition between members and nonmembers
 Relatively simple, fast and adaptive
 Less sensitive to system fluctuations
 Can implement design objectives, difficult to express
mathematicall in linguistic
mathematically,
ling istic or descriptive
descripti e rules.
r les
Fuzzy Logic, Sets and Systems
Wh F
Why
Fuzzy
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Approximate and inexact nature of the real word; vague
concepts easily dealt with by humans in daily life.
Fuzzy Logic, Sets and Systems
Wh F
Why
Fuzzy
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 Complex, ill-defined processes difficult for description and
analysis by exact mathematical techniques.
 Tolerance of imprecision in return for tractability, robustness,
and short computation time.
 Thus, we need other technique, as supplementary to
conventional
ti l quantitative
tit ti methods,
th d for
f manipulation
i l ti off vague and
d
uncertain information, and to create systems that are much closer
in spirit to human thinking.
thinking
Fuzzy logic is a strong candidate for this purpose.
purpose
Fuzzy Logic, Sets and Systems
Advantages and Drawbacks of Fuzzy Logic
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
Advantages
 Foundation for a general theory of commonsense reasoning
 Many practical applications
 Natural use of vague
g and imprecise
p
concepts
p
 Hardware implementations for simpler tasks

Drawbacks
 Formulation of the task can be very tedious
 Membership functions can be difficult to find
 Multiple ways for combining evidence
 Problems with long inference chains
 Efficiency for complex tasks
 There are many ways of interpreting fuzzy rules, combining the
outputs of several fuzzy rules and de-fuzzifying the output.
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Application Domains
 Fuzzy Logic
 Fuzzy Control
 Neuro - Fuzzy System
 Intelligent
g
Control
 Hybrid Control
 Fuzzy Pattern Recognition
 Fuzzy
F
Modeling
M d li
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Some Interesting Applications
 Sendal
S d l subway
b
(Hitachi)
(Hit hi)
 Elevator Control (Fujitec, Hitachi, Toshiba)
 Sugeno's
g
model car and model helicopter
p
 Hirota's robot
 Nuclear Reactor Control (Hitachi, Bernard)
 Automobile
A t
bil automatic
t
ti transmission
t
i i (Nissan,
(Ni
Subaru)
S b )
 Bulldozer Control (Terano)
 Ethanol Production (Filev)
(
)
 Appliance control
• Washing machine
• Microwave
• Ovens
• Rice cookers (temperature control)
• Vacuum
V
cleaners
l
• Camcorders and Digital Image Stabilizer (auto-focus and jiggle control)
• TVs,
• Copier quality control
• Air-conditioning systems
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The Major Research Fields in Fuzzy Theory
Fuzzy Logic, Sets and Systems