page hits since 29.01.2000

     
                   (2nd year, 4 credit hours, 42 h lectures)  
   
                   (4th year Technical Elective, 4 credit hours, 42 h lectures)   
     
                   (4th year Technical Elective, 4 credit hours, 42 h lectures)
     
                   (2nd year, 4 credit hours, 42 h lectures)

     Lecture Materials, Examples and Course Slides
        (.doc and .ppt formats)
     MATLAB examples (lecture material)
        (screenshots of the programs prepared in MATLAB 5.2)
     Commercial and free software «fuzzy» packages
        (fuzzyTECH, CubiCalc, FL Toolboxes)
     Project (CMPE-401):  Simple INference Engine (SINE 1.0)
        (June 2000)
     Selected Journals and Series   (IFSA, IEEE),
        Conferences,Workshops and Seminars
     Selected Sections of Course Projects   (Spring' 2000)
     Fuzzy Logic related Courses in other Universities worldwide

       contents.doc

Final (Spring 1999/2000 academic year) Course contents prepared before classes started (Word 97 document, 2 pages), 114 Kb
Because of the lack of time, some of the topics (e.g. fuzzy events & measures, additive fuzzy systems) were not covered in the course (1999/2000 academic year) and were left for self-studying

       fuzzy.doc

Short explanations of fuzziness, fuzzy sets and fuzzy systems based on journal publications and books (Word 97 document, 4 pages), 90 Kb  

       slides.zip     [final version revised on July 12, 2000]

106 lecture slides (PowerPoint 2000 presentation; 1,33 Mb). Action settings for some buttons on the slides are disabled

  
      MS® PowerPoint Viewer 97 (2000 Release)

This version of MS® PowerPoint Viewer 97 (2000 Release) gives a chance for a user to view (display) and print files created in PowerPoint 2000 or in any previous version of PowerPoint package. The PP Viewer (2,7 Mb) is available for FREE downloading  (updated on August 27, 1999)
      

       file1.zip
       file2.pdf

Fuzzy Systems, Modeling and Identification by Dr.Robert Babuska (EE Department, Delft University of Technology, The Netherlands)
Lecture Notes (72 Slides, file fuzzmod.zip) and the text (37 pages, file fuzzmod.pdf) were prepared for the course «Fuzzy Logic for Engineering Applications»

       Data Engineering

Lecture Notes by Dr.Olaf Wolkenhauer (Department of Electrical Engineering & Electronics, Control Systems Centre, UMIST). This course covers such topics as systems analysis, fuzzy systems identification, fuzzy inference engines,
fuzzy mathematics, etc. (all notes are available in .pdf fomat)

  
      Adobe Acrobat Reader (v.4.05b)

You can get Adobe® Acrobat® Reader (software for viewing and printing documents in Adobe Portable Document Format (PDF)) here. The current version available for FREE downloading is 4.05b (English)
      

       fuzreas.zip     [requires changes and modifications]

Fuzzy IF-THEN rules. Fuzzy Reasoning (example). Includes 3 Word 97 files. Explanations use CubiCalc and fuzzyTECH demo versions  (see links below). The following files are in archive:  fuzzy_11.doc (448Kb), fuzzy_12.doc (1,62Mb) and fuzzy_13.doc (1,26Mb); each document (Word 97) consists of 3 pages. It should be noted (!!) that the example of the system "deflection angle of the acceleration pedal - speed of the car" has very serious deficiencies (as a result of a poor design). Students have to propose their own modifications and to explain them... 

  
Simple INference Engine (SINE, version 1.0) was written by Waseem Khalil (Spring' 2000 graduate). This program implements a fuzzy rule-based inference using generalized Modus Ponens scheme. Current version supports 4 basic Inference Engines (Zadeh, Lukasiewicz, Minimum and Product), however a user can "enlarge" in a way this list by manual selection of corresponding t- and s-norms, implications and combinations from Control form. Convenient MF Editor visualizes a choice of membership functions (4 different types for now) and their parameters. Defuzzification process uses Centroid (COA) and Mean-of-Maximum (MOM) methods. Help options provide both brief explanation of fuzzy systems and inference mechanism and guidance through the main working steps of the program.

       sinefuz1.zip

If You have found any errors or deficiencies in the program, please, let us know about them (e-mail).
The final version of SINE 1.0 (for single input - single output system) was released on June 16, 2000. The size of the zip-file is only 340 Kb (after decompression the only file takes 1,42 Mb of the disk space)
   
     

       LExamples

MATLAB Examples discussed in the class:       
     (MATLAB slide 1)   operations on fuzzy sets, 
     (MATLAB slide 2)   linguistic hedges; Gaussian, bell-shaped and sigmoidal
             membership functions (effect of parameters changes)
     (MATLAB slide 3)   fuzzy implication as a conjunction; Mamdani and
             Larsen implications     
     (MATLAB slide 4)   implication operators (examples of fuzzy implication
             functions)     

       Soft Computing Toolbox

(MATLAB version 4&5) used in the book «Neuro-Fuzzy and Soft Computing» by J.-S.R.Jang, C.-T.Sun and E.Mizutani (Prentice Hall, 1997). The same collection (software companion) of MATLAB scripts can be obtained from the MathWorks Library (ftp site). Slides for instructors (Fuzzy Sets (chapter 2 of the book), Fuzzy Rules and Fuzzy Reasoning (chapter 3) and Derivative-Free Optimization (chapter 7)) in ppt or HTML format can be found here as well

       Fuzzy Logic Toolbox

(MATLAB version 5) designed in the Control Lab of Delft University of Technology, The Netherlands

       fuzzyTECH
  
A family of software development tools for fuzzy logic and neuro-fuzzy solutions from INFORM (a fully functional demo version of fuzzyTECH Release 5.31f (May 23, 2000) is available for downloading).
The program includes a convenient Fuzzy Design Wizard that guides the design of fuzzy system's prototype and visualizes results (Project Editor). Linguistic Variable Editors (LVE) are used for creating and graphical editing of membership functions (LV Wizard included). Interactive Debugging (one of the forms supported by fuzzyTECH) helps in checking of system's work and in graphical viewing of inference process (modification of MFs can be done «on fly»). Visualization of firing degrees of the rules (weights of rules or Degrees of Support (DoS) are modifiable at the debugging stage) and defuzzification (if necessary, defuzzification method can be changed in the interactive debugging mode as well). FuzzyTECH uses original Fuzzy Technology Language (FTL) format for storing designed fuzzy systems on the disk.   
NeuroFuzzy Module provides training facilities for components of the fuzzy system on the base of sample data or/and a priori knowledge. Further manual optimization of the system can be done...
fuzzyTECH supports several ways of its integration with other software packages, i.e. MS Excel, MS Access, Visual Basic, C/C++, Delphi (in debug modes ASCII formatted data files are accessible through fuzzyTECH)

       CubiCalc

An interactive shell for creating and using fuzzy rules from HyperLogic Corp.  (demo version with disabled data saving/exporting features is available for downloading). Technical Notes on Inference Techniques in CubiCalc can be found here

       Fuzzy Logic Toolbox 2.0     

A graphical environment for designing fuzzy systems (requires MATLAB) from MathWorks, Inc. Here is what Prof. L.A.Zadeh said about Fuzzy Logic Toolbox (MATLAB Conference, 1995)

       JFS (version 2) is a free fuzzy systems tool (Windows 95/98/NT) by J.E.Mortensen

       FUZZLE 3.0  (Fuzzy Logic Tool)     

A PC-based development shell for fuzzy if-then type rules from MODiCO Inc. (animated demo version, 1.05 Mb file, provides a general overview of the product's facilities). It supports its own execution module (with graphical vizualization) and converter to ANSI C/Fortran code. Both numeric and linguistic data entries are supported. Main steps of development in FUZZLE are explained on the company's page (here You'll find also unlocking password for the program). Full installation under Windows 95/98 required about 19 Mb of HD space. The package is supplied with 8 animated tutorials («silent video clips») that cover all working aspects

   
«The Achilles' heel of a fuzzy system is its rules. Smart rules give smart systems and other rules give less smart or even dumb systems.
...Adaptive fuzzy systems can help automate this process by using neural networks or neural-like learning algorithms to tune rules and thus to move the fuzzy rule patches in the state space. ...Neural networks can learn from data and feedback; however, understanding the knowledge or the pattern learned by the neural networks has been difficult.
...In contrast, fuzzy rule-based models are easy to comprehend because it uses linguistic terms and the structure of if-then rules. Unlike neural networks, however, fuzzy logic does not come with a learning algorithm. ...A neuro-fuzzy system can be loosely defined as a system that uses a combination of fuzzy logic and neural networks».

B.Kosko. Fuzzy Engineering, Prentice Hall, 1997 ©
  J.Yen, R.Langari. Fuzzy Logic. Intelligence, Control, and Information, Prentice Hall, 1999 ©
         

     PROJECT 1 (part of the CMPE-586 course project) is done by
             Hashem Lababidi (monitor of the group), Roustem Nizamiev and Zeki Yetgin
        

    
    Brief problem specification:   In ATM, during the call set-up phase, the user declares its traffic characteristics (requirements) to network in the form of traffic contract, which includes the transfer rate. Because of statistical multiplexing and the absence of flow control between the user and the network, a call may exceed the negotiated transfer, and this leads to congestion problems. In order to protect the network and connections from congestion, a network function called Usage Parameter Control (UPC) or, shortly, policing function, is needed. This policing mechanism must take certain actions when violation of the contract is detected. One of the most famous and the only implemented up-to-date policing mechanism is the Leaky Bucket (and its modified version, which uses Previous Data Gathering (PDG) block as an important component). Details of the Leaky Bucket mechanism («the most effective traditional policer up to now») are shown in the Figure 1 above. To enter the network an arriving cell must obtain a token from a token queue; if there is no token available, an arriving cell is deemed (violation of the traffic contract). Unfortunately, this approach have problems with policing of well-behaving source (synchronization with the traffic source is absent).
A modified version of the Leaky Bucket mechanism is synchronized with the source (see Figure 2 below). PDG unit takes a decision and trigger data buffer with a Boolean result.
   

    Definition of the Fuzzy System (Fuzzy PDG Unit):    Consider a transfer rate from the previous bursts (BehaviorRate) as an input for FPDG unit, whereas the size of buffer (BufferSize) is a unit's output. The input domain is a closed interval [0,60] (cells/unit), the output domain is [0,100] (a buffer size greater than 100 increases the average cell delay, which is not desirable). Definitions of linguistic variables and terms, rule base and inference process are covered by Borland Delphi 4 implementation:

   
       fuzst3.exe    [self-extracting file, 341 Kb]
    
The final version of the program was submitted on June 19, 2000. Results of performed tests (fuzzyTECH 5.31 and SINE 1.0) are included (in the form of screenshots) into the PDF-document (fuzst3.pdf, 576 Kb).

    
Additional sources of information (Leaky Bucket Mechanism):
1.  CS-791 - A Critical Look at Network Protocols by Prof. John Byers, October 28, 1999
2.  Scheduling and Policing Mechanisms (chapter 6.6) in «Computer Networking. A Top-Down Approach Featuring the Internet» by J.F.Kurose and K.W.Ross
3.  The Leaky Bucket as a Policing Device: Transient Analysis and Dimensionings by D.Logothetis and K.S.Trivedi
  

     PROJECT 2 (part of the CMPE-586 course project) is done by
             Hasan Sarper (monitor of the group) and Ahmet Akarsu
      

    Brief problem specification:   When a program executed on a single computer becomes inefficient in trying to compute the result of a complex task, we can partition the task into several subtasks and distribute them between computers that work in parallel to minimize amount of time needed to complete all calculations. This way of using computers in cooperation is called parallel computation. At this point reasonable questions may come to our mind: what is the functional dependency between the number of computers and the corresponding amount of time necessary to complete a program's execution? will the performance of «enlarged» system grow in linear proportion to the number of computers used? Unfortunately, the answer to the second question is negative - for any task, with any complexity, the overall performance of the parallel system increases as the number of computers grows, but this goes on up to some extremum point (depends upon the complexity of the task). After it, with a growth of the number of computers, the performance will decrease due to communication and coordination overheads in the system. The Figure given above illustrates an approximate functional dependency «number of computers - time» for two tasks of different complexities (complexity(task2)>complexity(task1)). In both cases functions have parabolic-like shape.  

    Definition of the Fuzzy System:   Consider the number of computers (1..8) as an input variable of the system; 7 linguistic terms are chosen as values of input variable (e.g. one computer is associated with the value negligible, whereas two computers correspond to the restricted case as a starting point for parallel computations, etc.). Computational time is a system's output; the output domain is [40,60] (measured in milliseconds). In the current implementation the complexity of the task is fixed (constant), however, later on (!) it will form the second input variable. Definitions of linguistic variables and their terms (antecedent and consequent MFs), rule base and inference process details are covered by group's MATLAB 5.3 (Release 11) application (a set of M- and MAT-files) enhanced with a convenient GUI:

  
       sarpak1.exe    [self-extracting file, 45 Kb]
    
The final version of the program was submitted on June 20, 2000. After extracting 14 files and saving them in the arbitrary directory on the disk, run MATLAB 5.3 and add a full path (option File > Set Path...) to the directory used; afrewards, run script SarpAk.m. The general idea of designed Graphical User Interface can be obtained from the file (sarpak1.pdf, 320 Kb), which includes several screenshots of selected forms.

   
«Parallelism is that simple - applying multiple CPUs to a single problem. Besides offering faster solutions, applications that have been parallelized can solve bigger, more complex problems whose input data or intermediate results exceed the memory capacity of one CPU.
...Computer scientists may find parallel programming to be interesting in itself, but that's not the objective of most scientists and engineers. As Boeing's Ken Neves said, "Nobody wants parallelism. What we want is performance".
...Is parallel performance achievable? Absolutely. But it is not easily achieved, nor can it be achieved for every problem. Achieved performance depends on five interdependent factors:
1.  the degree of parallelism inherent in the application;
2.  the parallel computer architecture on which that application executes;
3.  how well the language and runtime system exploit that architecture;
4.  how effectively the program code exploits the language, runtime system, and architecture; and
5.  the runtime environment at the time of execution».

C.M.Pancake (Oregon State University), IEEE Computational Science & Engineering, vol.3, #2, 1996, pp.18-37 © 
         

     PROJECT 3 (part of the CMPE-586 course project) is done by
             Önsen Toygar (monitor of the group), Öykü Akaydin and Meltem Yagli

    
    Brief problem specification and definition of the Fuzzy System:   Very often recommendations on the desired «healthy» correspondence between height and weight given by doctors (dietologists), aerobics instructors and other specialists to women are not precise (uncertain in some particular cases). It is a regular practice in recommendations to use such terms/phrases as «close to», «around», «quite light (normal)», «too heavy for the average height», etc. For this section of the course project the age range is limited to (20..34), whereas the height covers quite realistic domain of values from 1.5 to 1.82 meter long. A woman's age is an input variable of the system (the variable has 5 linguistic values); appropriate weight is a system's output (5 adjectives very light, light, normal, heavy and very heavy characterize this variable). The Figure shown above illustrates one of numerous data tables, which cover ideal (!?) characteristics of interest for women - other sources propose slightly different values of weight. The latter somehow depends on the region, habits, traditions (including cuisine), etc. Definitions of linguistic variables and their terms (antecedent and consequent MFs), rule base and inference process details are covered by Borland Delphi 4 implementation:

 
       heiweig.zip    [a single file in zip-format, 278 Kb]
    
The final version of the program was submitted on June 20, 2000. The program does not display 3D relations (this was done separately in MATLAB environment). The age of women under consideration is fixed (limited to the range with very close values of weight), but it may form the second system's input variable. Conclusions produced by the program were compared to the output of fuzzyTECH 5.31 and running MATLAB script (M-file prepared by the group) for several test data (similarity is 97%).    

     PROJECT 4 (part of the CMPE-586 course project) is done by
Yiltan Bitirim, Arca Artem and Tamer Tulgar (monitor of the group)
      

     
    Brief problem specification:   A speed of file's downloading may vary depending on many factors, e.g. connection speed of the user's local site to the Internet, number of connected users to the site, traffic intensity of the site in a certain period of day, etc. The Figure shown above represents experimental data obtained on May 29/30, 2000 (these were the days when there were problems with satelite connection). It is better to say that the Figure shows a tendency of changes in downloading speed through the day. «One-day» experiments (in the same working conditions) were repeated during the month of June (different sites and sizes of files), but the results were very similar (late in the night (00:00 - 03:30am) we were able to notice short time «splashes» of speed up to 9.06 Kb).

    Definition of the Fuzzy System:   Consider the period of the day (0..24h) as an input variable of the system; 8 linguistic terms are chosen as values of input variable (e.g. late night, early morning, morning, etc.). File downloading speed is a system's output; the output domain is [0,9] (measured in kilobytes per second). Definitions of working conditions, linguistic variables and their terms (antecedent and consequent MFs), rule base and inference process (two predefined inference engines are used, i.e. minimum engine and product engine) details are covered by group's MATLAB 5.3 (Release 11) application (with GUI):

        
       loaddown.exe    [self-extracting file, 44 Kb]
    
The final version of the program was submitted on June 19, 2000. After extracting 30 M-files and 1 MAT-file and setting path in MATLAB environment, run script StartTask.m (  our apologizes for possible dislocation of forms images on the screen caused by   screen resolution).

     PROJECT 5 (part of the CMPE-586 course project) is done by
Mirza Faisal Baig (monitor of the group) and Mirza Tariq Hamayun (EE Department)
    

    Brief problem specification:   The downward velocity of landing aircraft is proportional to the square of the height. The aircraft will descend from altitude promptly, but it will touch down very gently to avoid damage. Two state variables for the simulation are height (h) and vertical velocity () of the aircraft (see Figure 1 above). The output of the system is a force f, which altered height and velocity of aircraft. In difference notation the new values of state variables and h are calculated in response to control input and the previous state variables values (see Figure 2). The task is to control aircraft's vertical descent during approach and landing (consider initial 0-th altitude of 1,000 feet (304.8m) and downward velocity of -20ft/s, or -6.1m/s).
     

  A fragment of FIS Editor (Fuzzy Logic Toolbox, MathWorks®)
      

    Definition of the Fuzzy System (Aircraft Landing Control):   The system under study has 2 inputs and one output (see Scheme above); membership functions for all 3 variables, definition of rules (totality of 20 rules), used operators, implication forms and deffuzification methods, results of simulation are distinctly shown by group's Fuzzy Logic Toolbox 2.0 implementation (Fuzzy Inference System, MATLAB 5.3, Release 11):

         
       aircraft.exe    [self-extracting file, 34 Kb]
    
The final version of the program was submitted on June 17, 2000. After extracting 10 M-files and 1 FIS file, run script air2aa2.m (  for better viewing enlarge Figure windows to the whole screen), or if You use FL Toolbox, run script fuzzy (it starts FIS Editor main window) and open from disk aircraft_2.fis (or, simply type fuzzy aircraft_2 in Run script dialog box).

   
«The Fuzzy inference system is a popular computing framework based on the concepts of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning... Because of its multi-disciplinary nature, the fuzzy inference system is known by a number of names, such as fuzzy-rule-based system, fuzzy expert system, fuzzy model, fuzzy associative memory, fuzzy logic controller, and simply (and ambiguously) fuzzy system.
...The basic structure of a fuzzy inference system consists of three conceptual components: a rule base, which contains a selection of fuzzy rules, a database or dictionary, which defines the membership functions used in the fuzzy rules, and a reasoning mechanism, which performs the inference procedure upon the rules and a given condition to derive a reasonable output or conclusion».

J.-S. Roger Jang, C.-T. Sun. Neuro-Fuzzy Modeling and Control (IEEE Proceedings, 1995) © 
 

          [interesting Internet sites related to Fuzzy Logic]

      
  Courses on Fuzzy Logic in other Universities worldwide:
    
     CpE 321:  Applied Fuzzy Logic I  (West Virginia University, Computer Science and Electrical Engineering, USA)
           Graduate Program in Computer Engineering (3 hrs. Lecture)
     EPS 3240:  Fuzzy Sets Theory and Fuzzy Logic  (Federal University of Santa Catarina State,
           Department of Production Engineering, Brazil). Includes Course Contents and Student Works
     MATH 5425:  Fuzzy Logic and Neural Nets  (The University of New South Wales, School of Mathematics, Australia)
           Graduate Course in Mathematics
     xxx:  Fuzzy Logic with Engineering Applications  (University of New Mexico, Department of Civil Engineering, USA)
     xxx:  Neural Fuzzy Systems  (Lectures by R.Fuller, Åbo Academi University, Finland)
   

     «Fuzzy Sets and Fuzzy Logic: Theory and Applications» by G.J.Klir and Bo Yuan   
                   (ISBN 0131011715)       NOTE:  This title is currently out of print
     «A First Course in Fuzzy Logic» by H.T.Nguyen and E.A.Walker  (ISBN 0849316596)
     «An Introduction to Fuzzy Logic for Practical Applications»
                    by K.Tanaka and T.Niimura  (ISBN 0387948074)
     «A Course in Fuzzy Systems and Control» by Li-Xin Wang  (ISBN 0135408822)
     «The Fuzzy Future: From Society and Science to Heaven in a Chip» by B.Kosko
                    (ISBN 0609604465)
     «The Fuzzy Systems Handbook: A Practioner's Guide to Building, Using, and
                    Maintaining Fuzzy Systems» by E.Cox   (ISBN 0121944557)
     «An Introduction to Fuzzy Sets: Analysis and Design (Complex Adaptive Systems)»
                    by W.Pedrycz and F.Gomide  (ISBN 0262161710)

      Fuzzy Sets and Systems  (by IFSA - International Fuzzy Systems Association)

      IEEE Transactions on Systems, Man, and Cybernetics  (by IEEE SMC Society)
      
                Part A: Systems and Humans     Part B: Cybernetics     Part C: Applications and Reviews

      IEEE Transactions on Knowledge and Data Engineering  (by IEEE Computer Society)

      The Handbooks of Fuzzy Sets Series  (by Kluwer Academic Publishers)
     
                volumes 1-7:
   
                   Fundamentals of Fuzzy Sets (Didier Dubois, Henri Prade, editors)
                   Mathematics of Fuzzy Sets (Ulrich Höhle, Stephen E. Rodabaugh)
                   Fuzzy Sets in Approximate Reasoning and Information Systems
                       (James C. Bezdek, Didier Dubois, Henri Prade, editors)
                   Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
                       (James C. Bezdek, James Keller, Raghu Krishnapuram, Nikhil R. Pal)
                   Fuzzy Sets in Decision Analysis, Operations Research and Statistics
                       (Roman Slowinski, editor)
                   Fuzzy Systems. Modeling and Control (Hung T. Nguyen, Michio Sugeno, editors)
                   Practical Applications of Fuzzy Technologies (Hans-Jürgen Zimmermann, editor)

      IEEE Intelligent Systems and Their Applications  (by IEEE Computer Society)

   
«Fuzzy Logic is a technology that mimics the human decision-making process on the very high abstraction level of natural language. On the contrary, neural nets try to copy the way a human brain works on the lowest level, the «hardware» level. ...The objective of a neural net is to process the information in the way in which it has been trained. Training involves either sample data sets of inputs and corre