Hamidreza Rashidy Kanan. Electrical Engineering Department, Bu-Ali Sina University

Transcription

1 Fuzzy Logic, Sets and ds Systems Lecture 1 Introduction Hamidreza Rashidy Kanan Assistant Professor, Ph.D. Electrical Engineering Department, Bu-Ali Sina University h.rashidykanan@basu.ac.ir; kanan_hr@yahoo.com

2 2

3 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, [2] Timothy J. Ross, Fuzzy Logic with Engineering g Applications,John Wiley & Sons, 2004.

4 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.

5 5 Syllabus 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 Rule Base and dfuzzy Inference Engine Fuzzifiers and Defuzzifiers

6 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 Clustering

7 7 Professional Organizations and Networks International Fuzzy Systems Association (IFSA) Japan Society for Fuzzy Theory and Systems (SOFT) Berkeley Initiative in Soft Computing (BISC) North hamerican Fuzzy Information Processing Society (NAFIPS) Spanish Association of Fuzzy Logic and Technologies The European Society for Fuzzy Logic and Technology (EUSFLAT) EUROFUSE Hungarian Fuzzy Society EUNITE

8 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 Mathware and dsoft ftcomputing 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)

9 9 Main Components of an Expert System

10 10 Main Components of an Expert System Knowledge Base Contains essential information about the problem domain Often represented as facts and rules 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 end users Development and maintenance of the knowledge base

11 Why Fuzzy 11 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 mathematically, in linguistic istic or descriptive e rules.

12 Why Fuzzy 12 Approximate and inexact nature of the real word; vague concepts easily dealt with by humans in daily life.

13 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 quantitative methods, for manipulation of vague and uncertain information, and to create systems that are much closer in spirit to human thinking. Fuzzy logic is a strong candidate for this purpose.

14 14 Advantages and Drawbacks of Fuzzy Logic Advantages Foundation for a general theory of commonsense reasoning Many practical applications Natural use of vague and imprecise concepts 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.

15 15 Application Domains Fuzzy Logic Fuzzy Control Neuro - Fuzzy System Intelligent Control Hybrid Control Fuzzy Pattern Recognition Fuzzy Modeling

16 16 Some Interesting Applications Sendal subway (Hitachi) Elevator Control (Fujitec, Hitachi, Toshiba) Sugeno's model car and model helicopter Hirota's robot Nuclear Reactor Control (Hitachi, Bernard) Automobile automatic ti transmission i (Nissan, Subaru) Bulldozer Control (Terano) Ethanol Production (Filev) Appliance control Washing machine Microwave Ovens Rice cookers (temperature control) Vacuum cleaners Camcorders and Digital Image Stabilizer (auto-focus and jiggle control) TVs, Copier quality control Air-conditioning systems

17 17 The Major Research Fields in Fuzzy Theory