Course detail

Fuzzy Systems for Control and Modelling

FIT-FSYAcad. year: 2013/2014

Motivation, crisp sets and fuzzy sets. Fuzzy sets operations, t-norms and conorms. Fuzzy relations and operations with them. Projection, cylindrical extension, composition. Approximate reasoning. Linguistic variable. Fuzzy implication. Generalized modus ponens and fuzzy rule "if-then". Inference rules. The evaluation of a set of the fuzzy rules. Fuzzy systems Mamdani and Sugeno. The structure of the system, knowledge and data base. Fuzzification and defuzzification. Fuzzy system as an universal approximator. Adaptive fuzzy systems, neuro fuzzy systems.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Pavel Jura, CSc.

Department

Department of Control and Instrumentation (UAMT)

Learning outcomes of the course unit

The student has fundamental knowledge and skill in the fuzzy theory. He knows to apply it in the field of the modelling and control of the uncertainty defined systems.

Prerequisites

There are no prerequisites

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course uses teaching methods in form of Lecture - 2 teaching hours per week, Projects - 1 teaching hour per week.

Assesment methods and criteria linked to learning outcomes

Working out of the project.

Course curriculum

    Syllabus of lectures:
    • Motivation, crisp sets and fuzzy sets.
    • Operation with the fuzzy sets.
    • t-norm a conorm.
    • Fuzzy relation and operations with them. Projection, cylindrical extension, composition.
    • Approximate reasoning. Linguistic variable. Fuzzy implication.
    • Generalised "modus ponens", fuzzy rule "if-then". Inference rules.
    • Evaluation of the set of fuzzy rules.
    • Fuzzy systems Mamdani a Sugeno.
    • The structure of the fuzzy system, knowledge and data base.
    • Fuzzification and defuzzification.
    • Fuzzy system is an universal approximator.
    • Adaptive fuzzy systems.
    • Neuro-fuzzy systems.

    Syllabus - others, projects and individual work of students:
    Mamdani or Sugeno type model in one implemented example.

Work placements

Not applicable.

Aims

The goal of the course is to acquaint with the fundamentals of fuzzy sets theory and fuzzy logic. Students learn to apply the fuzzy theory for modelling of te uncertainty systems. They acquaint with adaptive techniques in the fuzzy systems.

Specification of controlled education, way of implementation and compensation for absences

One mid-semestr written test.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Jura, P.: Základy fuzzy logiky pro řízení a modelování, VUTIUM Brno, 2003, ISBN 80-214-2261-0. Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Logic, Springer-Verlag, 1993, ISBN 3-540-56362-8. Novák, V.: Fuzzy množiny a jejich aplikace, Matematický seminář, SNTL Praha, 1986. Pokorný, M.: Řídicí systémy se znalostní bází, Skriptum VŠB TU Ostrava, 1995, ISBN 80-7078-275-7. Pokorný, M.: Umělá inteligence v modelování a řízení, Nakladatelství BEN, Praha, 1996, ISBN 80-901984-4-9. Vysoký, P.: Fuzzy řízení, skriptum FEL ČVUT Praha, 1996, ISBN 80-01-01429-8.

Recommended reading

Jura, P.: Základy fuzzy logiky pro řízení a modelování, VUTIUM Brno, 2003, ISBN 80-214-2261-0. Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Logic, Springer-Verlag, 1993, ISBN 3-540-56362-8. Novák, V.: Fuzzy množiny a jejich aplikace, Matematický seminář, SNTL Praha, 1986. Pokorný, M.: Řídicí systémy se znalostní bází, Skriptum VŠB TU Ostrava, 1995, ISBN 80-7078-275-7. Pokorný, M.: Umělá inteligence v modelování a řízení, Nakladatelství BEN, Praha, 1996, ISBN 80-901984-4-9. Vysoký, P.: Fuzzy řízení, Skriptum FEL ČVUT Praha, 1996, ISBN 80-01-01429-8.

Classification of course in study plans

  • Programme IT-MSC-2 Master's

    branch MBI , 0 year of study, summer semester, elective
    branch MBS , 0 year of study, summer semester, elective
    branch MGM , 0 year of study, summer semester, elective
    branch MIN , 0 year of study, summer semester, elective
    branch MIS , 0 year of study, summer semester, elective
    branch MMI , 0 year of study, summer semester, elective
    branch MMM , 0 year of study, summer semester, elective
    branch MPV , 0 year of study, summer semester, elective
    branch MSK , 0 year of study, summer semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Pavel Jura, CSc.

Syllabus

  • Motivation, crisp sets and fuzzy sets.
  • Operation with the fuzzy sets.
  • t-norm a conorm.
  • Fuzzy relation and operations with them. Projection, cylindrical extension, composition.
  • Approximate reasoning. Linguistic variable. Fuzzy implication.
  • Generalised "modus ponens", fuzzy rule "if-then". Inference rules.
  • Evaluation of the set of fuzzy rules.
  • Fuzzy systems Mamdani a Sugeno.
  • The structure of the fuzzy system, knowledge and data base.
  • Fuzzification and defuzzification.
  • Fuzzy system is an universal approximator.
  • Adaptive fuzzy systems.
  • Neuro-fuzzy systems.

Project

26 hod., optionally

Teacher / Lecturer

prof. Ing. Pavel Jura, CSc.