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.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Entry knowledge

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

Rules for evaluation and completion of the course

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

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.
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

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

JURA, P.; Základy fuzzy logiky pro řízení a modelování, Brno VUTIUM, 2003, 132 s. ISBN 80-214-2261-0. (CS)
JURA,P. Slajdy přednášek předmětu MFSY (CS)

Not applicable.

eLearning

Classification of course in study plans

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

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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.
Neuro-fuzzy systems.

Exercise in computer lab

13 hours, compulsory

Teacher / Lecturer

Syllabus

Education program for fuzzy logic. Tests in the education program. Fuzzy toolbox for Matlab.
Demonstration examples in Fuzzy toolbox Matlab.
Individual solving of a simple task. Project definition a its individual solving.

Project

13 hours, compulsory

Teacher / Lecturer

Syllabus

Mamdani or Sugeno type model of a practicle example.

eLearning