Course detail

# Fuzzy Systems

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

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.

Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Logic. Springer-Verlag, 1993. (EN)
Klir, G.J., Bo Yuan.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall PTR, 1995. (EN)
Kosko B.: Neural Networks and Fuzzy Systems. A Dynamical Systems Approach to Machine Intelligence. Prentice Hall Int., 1992 (EN)
Li-Xi Wang: Adaptive fuzzy systems and control. Design and stability analysis. PTR Prentice Hall Inc., 1994. (EN)
Lin,C.,T.: Neural Fuzzy Control Systems with Structure and Parameter Learning. World Scientific, Singapore, 1994. (EN)
Pedrycz W.: Fuzzy Control and Fuzzy Systems. Second, extended edition. John Wiley &Sons, New York,1993. (EN)
Jura.P.: Základy fuzzy logiky pro řízení a modelování, nakladatelství VUTIUM 2003. (EN)

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 smester.
Project 30 points.
Final written test 55 points.

Language of instruction

English

Work placements

Not applicable.

Course curriculum

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.
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 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

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 EEKR-MN Master's

branch MN-KAM , 1. year of study, summer semester, 5 credits, optional specialized

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

13 hours, compulsory

Teacher / Lecturer

The other activities

13 hours, compulsory

Teacher / Lecturer

eLearning