Course detail

Fuzzy Systems

FEKT-MPC-FSYAcad. year: 2020/2021

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.

Learning outcomes of the course unit

An absolvent is able to:
- explain the difference between classical and fuzzy set
- explain the notion linguistic variable
- apply the operation with fuzzy sets to mathematical description of approximate reasoning
- name and explain attributes of set of fuzzy rules
- name and explain two types of fuzzy systems
- explain the function of fuzzy system as a universal approximator
- describe of adaptation in the fuzzy systems


The basic knowledge of set theory and logic, basic knowledge of system theory and control theory (on the level of bachelor's study)


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

JURA, P.; Základy fuzzy logiky pro řízení a modelování, Brno VUTIUM, 2003, 132 s. ISBN 80-214-2261-0. (CS)
DRIANKOV, D.; HELLENDOORN, H.; REINFRANK, M. An Introduction to Fuzzy Logic. Springer-Verlag, 1993. 316 p. ISBN 3-540-56362-8. (EN)
KLIR, G.J.; BO YUAN. Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice Hall PTR, 1995. 574 p. ISBN 0-13-101171-5. (EN)
ZADEH, L.A. Fuzzy sets. Information and Control 8, pp. 338-353, (1965) (CS)
ZADEH, L.A.. From Computing with Numbers to Computing with Words—From Manipulation of Measurements to Manipulation of Perceptions. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 45, NO. 1, JANUARY 1999, pp. 105-119. (CS)
ZADEH, L.A. Fuzzy logic—a personal perspective. Fuzzy Sets and Systems 281 (2015) 4-20, pp.4-20. (CS)
SUBBULAKSHMI, K. Antilock-Braking System Using Fuzzy Logic. Middle-East Journal of Scientific Research 20 (10) 2014, pp. 1306-1310. ISSN 1990-9233 (CS)
JURA,P. Slajdy přednášek předmětu MFSY (CS)

Planned learning activities and teaching methods

Teachning methods include lectures and computer laboratories. Students have to write a single project/assignment during the course.

Assesment methods and criteria linked to learning outcomes

Written test- 15 points during semester.
Project- 20 points.
Final written test- 65 points.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Motivation, crisp sets and fuzzy sets.
2. Operation with the fuzzy sets.
3. t-norm a t-conorm.
4. Fuzzy relation and operations with them. Projection, cylindrical extension, composition.
5. Approximate reasoning. Linguistic variable. Fuzzy implication.
6. Generalised modus ponens, fuzzy rule if-then. Inference rules.
7. Evaluation of the set of fuzzy rules.
8. Fuzzy systems Mamdani a Sugeno.
9. The structure of the fuzzy system, knowledge and data base.
10. Fuzzification and defuzzification.
11. Fuzzy system is an universal approximator.
12. Adaptive fuzzy systems.
13. Neuro-fuzzy systems.


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

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

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

  • Programme MPC-KAM Master's, 1. year of study, summer semester, 6 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

13 hours, compulsory

Teacher / Lecturer


13 hours, compulsory

Teacher / Lecturer