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.
Supervisor
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
Prerequisites
The basic knowledge of set theory and logic, basic knowledge of system theory and control theory (on the level of bachelor's study)
Co-requisites
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
Czech
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.
Aims
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