i S d Si S d SFuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

LectureLecture 11Lecture Lecture 11IntroductionIntroduction

Hamidreza Rashidy KananAssistant Professor Ph DAssistant Professor, Ph.D.

Electrical Engineering Department, Bu-Ali Sina University

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

h.rashidykanan@basu.ac.ir; kanan_hr@yahoo.com

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Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

3 Course Information

Evaluation Policy

Final Exam 70% Project 30%Project 30%

Text/Reference Books

[1] Li Xin Wang, “A course in fuzzy systems and control”,Prentice Hall 1997Prentice-Hall, 1997.

[2] Timothy J. Ross, “Fuzzy Logic with Engineering

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

[ ] y , y g g gApplications”,John Wiley & Sons, 2004.

4 Course Information ObjectiveTo provide a basic understanding of the:To provide a basic understanding of the:

Fuzzy Logic, Sets and their mathematics. Design methods of Fuzzy systems. Some applications of Fuzzy systems.

Pre-requisitesCalculus and MATLAB Software.

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

5 Syllabus

Introduction The Mathematics of Fuzzy Systems Fuzzy Sets and Basic Operations on Fuzzy Sets Fuzzy Sets and Basic Operations on Fuzzy Sets Further Operations on Fuzzy Sets Fuzzy Relations and the Extension Principle Fuzzy Relations and the Extension Principle Linguistic Variables and Fuzzy IF-THEN Rules Fuzzy Logic and Approximate Reasoning Fuzzy Logic and Approximate Reasoning

Fuzzy Systems and Their Properties F R l B d F I f E i Fuzzy Rule Base and Fuzzy Inference Engine Fuzzifiers and Defuzzifiers

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6 Syllabus

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

Fuzzy Classification and Clusteringy g

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7 Professional Organizations and Networks

International Fuzzy Systems Association (IFSA) Japan Society for Fuzzy Theory and Systems (SOFT) Berkeley Initiative in Soft Computing (BISC) h A i f i i S i ( A S) North American Fuzzy Information Processing Society (NAFIPS) Spanish Association of Fuzzy Logic and Technologies Th E S i t f F L i d T h l (EUSFLAT) The European Society for Fuzzy Logic and Technology (EUSFLAT) EUROFUSE Hungarian Fuzzy Society Hungarian Fuzzy Society EUNITE

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8 Fuzzy Logic Journals

Journal of Fuzzy Sets and Systems The Journal of Fuzzy Mathematics The Journal of Fuzzy Mathematics International Journal Uncertainty, Fuzziness and Knowledge-Based Systems IEEE Transactions on Fuzzy Systems International Journal of Approximate Reasoning International Journal of Approximate Reasoning Information Sciences International Journal of Intelligent Systems M th d S ft C ti Mathware and Soft Computing Journal of Advanced Computational Intelligence & Intelligent Informatics Journal of Intelligent & Fuzzy Systems Soft Computing Electronic Transactions on Artificial Intelligence (ETAI) Biological Cybernetics Biological Cybernetics International Journal of Computational Intelligence and Applications (IJCIA) International Journal of Intelligent Control and Systems (IJICS)

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

9 Main Components of an Expert System

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

10 Main Components of an Expert System

Knowledge Base Contains essential information about the problem domain Often represented as facts and rulesp

Inference Engine Mechanism to derive new knowledge from the knowledge Mechanism to derive new knowledge from the knowledge

base and the information provided by the User Often based on the use of rulesOften based on the use of rules

User Interface Interaction ith end sers Interaction with end users Development and maintenance of the knowledge base

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

Wh F11

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 ling istic or descripti e r les

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mathematically, in linguistic or descriptive rules.

Wh F12

Why Fuzzy

Approximate and inexact nature of the real word; vague

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concepts easily dealt with by humans in daily life.

Wh F13

Why Fuzzy

Complex, ill-defined processes difficult for description andanalysis by exact mathematical techniques.

Tolerance of imprecision in return for tractability, robustness,and short computation time.

Thus, we need other technique, as supplementary toti l tit ti th d f i l ti f dconventional quantitative methods, for manipulation of vague and

uncertain information, and to create systems that are much closerin spirit to human thinkingin spirit to human thinking.

Fuzzy logic is a strong candidate for this purpose

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Fuzzy logic is a strong candidate for this purpose.

14 Advantages and Drawbacks of Fuzzy Logic

Advantages Foundation for a general theory of commonsense reasoning Foundation for a general theory of commonsense reasoning Many practical applications Natural use of vague and imprecise conceptsg p p Hardware implementations for simpler tasks

Drawbacks Drawbacks Formulation of the task can be very tedious Membership functions can be difficult to find Membership functions can be difficult to find Multiple ways for combining evidence Problems with long inference chains Problems with long inference chains Efficiency for complex tasks There are many ways of interpreting fuzzy rules, combining the

Fuzzy Logic, Sets and SystemsFuzzy Logic, Sets and Systems

There are many ways of interpreting fuzzy rules, combining the outputs of several fuzzy rules and de-fuzzifying the output.

15 Application Domains

Fuzzy Logic Fuzzy Logic

Fuzzy Control Fuzzy Control Neuro - Fuzzy System Intelligent Controlg Hybrid Control

Fuzzy Pattern Recognition

F M d li Fuzzy Modeling

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16 Some Interesting Applications S d l b (Hit hi) Sendal subway (Hitachi) Elevator Control (Fujitec, Hitachi, Toshiba) Sugeno's model car and model helicopterg p Hirota's robot Nuclear Reactor Control (Hitachi, Bernard)A t bil t ti t i i (Ni S b )Automobile automatic transmission (Nissan, Subaru) Bulldozer Control (Terano) Ethanol Production (Filev)( )Appliance control

• Washing machine• Microwave• Microwave• Ovens• Rice cookers (temperature control)

V l• Vacuum cleaners• Camcorders and Digital Image Stabilizer (auto-focus and jiggle control)• TVs,

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• Copier quality control• Air-conditioning systems

17 The Major Research Fields in Fuzzy Theory

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