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
[email protected]; [email protected]
Fuzzy Logic, Sets and Systems
2
Fuzzy Logic, Sets and Systems
3
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.
Fuzzy Logic, Sets and Systems
4
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





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
6
 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
Fuzzy Logic, Sets and Systems
7









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
8















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)
Fuzzy Logic, Sets and Systems
9
Main Components of an Expert System
Fuzzy Logic, Sets and Systems
10
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
Fuzzy Logic, Sets and Systems
11
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
12
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
13
 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
14

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.
Fuzzy Logic, Sets and Systems
15
Application Domains
 Fuzzy Logic
 Fuzzy Control
 Neuro - Fuzzy System
 Intelligent
g
Control
 Hybrid Control
 Fuzzy Pattern Recognition
 Fuzzy
F
Modeling
M d li
Fuzzy Logic, Sets and Systems
16
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
Fuzzy Logic, Sets and Systems
17
The Major Research Fields in Fuzzy Theory
Fuzzy Logic, Sets and Systems