Course detail

Fuzzy systems

FEKT-MFSYAcad. year: 2011/2012

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

The basic knowledge of signals, systems and linear control theory

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Written test 15 points
Project 30 points
Final written test 55 points

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.
Adaptive fuzzy systems.
Neuro-fuzzy systems.

Work placements

Not applicable.

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.

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 (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-M Master's

    branch M-KAM , 1. year of study, summer semester, optional specialized

Type of course unit

 

Lecture

26 hours, 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.

Exercise in computer lab

13 hours, compulsory

Teacher / Lecturer

prof. Ing. Pavel Jura, CSc.

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.

The other activities

13 hours, compulsory

Teacher / Lecturer

prof. Ing. Pavel Jura, CSc.

Syllabus

Mamdani or Sugeno type model of a practicle example.