Course detail

Fuzzy Models of Technical Processes and Systems

FSI-9FMSAcad. year: 2024/2025

The course is intended for the students of doctoral degree programme and it is concerned with the fundamentals of the fuzzy sets theory: operations with fuzzy sets, extension principle, fuzzy numbers, fuzzy relations and graphs, fuzzy functions, linguistics variable, fuzzy logic, approximate reasoning and decision making, fuzzy control, etc. It also deals with the applicability of those methods for modeling of vague technical variables and processes.

Language of instruction

Czech

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Elements of the set theory, algebra and mathematical analysis.

Rules for evaluation and completion of the course

The exam is in form read report from choice area of fuzzy modeling or else elaboration of written work specialized on solving of concrete problems.
Attendance at lectures is not compulsory, but is recommended.

Aims

The course objective is to make students acquainted with basic methods and applications of fuzzy sets theory, that allows to model vague quantity of numerical and linguistic character, and subsequently systems and processes, which cannot be described with classical mathematical models.
Students acquire necessary knowledge of important parts of fuzzy set theory, which will enable them to create effective mathematical models of technical phenomena and processes with uncertain information, and carry them out on PC by means of adequate implementations.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Dubois, D. - Prade, H.: The Handbooks of Fuzzy Sets (Vol. 1-7). Dordrecht : Kluwer Academic Publishers, 2000. (EN)
Klir, G. J. - Yuan B.: Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey : Prentice Hall, 1995. (EN)
Zimmermann, H. J.: Fuzzy Sets Theory and Its Applications. Boston : Kluwer-Nijhoff Publishing, 1991. (EN)

Recommended reading

Kolesárová, A. - Kováčová, M.: Fuzzy množiny a ich aplikácie. Bratislava : Slovenská technická univerzita v Bratislave, 2004.
Novák, V.: Fuzzy množiny a jejich aplikace. Praha : SNTL, 1990.
Novák, V.: Základy fuzzy modelování. Praha : BEN, 2000.
Talašová, J.: Fuzzy metody ve vícekriteriálním rozhodování a rozhodování. Olomouc : Univerzita Palackého, 2002.

Classification of course in study plans

  • Programme D-APM-P Doctoral 1 year of study, winter semester, recommended course
  • Programme D-APM-K Doctoral 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

Fuzzy sets (motivation, basic notions, properties).
Operations with fuzzy sets (basic types, properties).
Triangular norms and co-norms.
Extension principle (Cartesian product, extension of mapping).
Fuzzy numbers (extended operations, properties, interval arithmetic).
Fuzzy relations and graphs (basic notions, types, properties).
Fuzzy functions (basic types, fuzzy parameter, derivation, integral).
Linguistic variable (model, properties, fuzzy presentation, defuzzification).
Fuzzy logic (multi-value logic, linguistic logic).
Approximate reasoning and decision-making (fuzzy control).
Selected fuzzy models: cluster analysis, linear programming, reliability etc.