Fuzzy Models of Technical Processes and Systems (FSI-9FMS)

Academic year 2022/2023
Supervisor: doc. RNDr. Libor Žák, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
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.
Learning outcomes and competences:
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.
Prerequisites:
Elements of the set theory, algebra and mathematical analysis.
Course contents:
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.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
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.
Controlled participation in lessons:
Attendance at lectures is not compulsory, but is recommended.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 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.
Literature - fundamental:
1. Klir, G. J. - Yuan B.: Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey : Prentice Hall, 1995.
2. Zimmermann, H. J.: Fuzzy Sets Theory and Its Applications. Boston : Kluwer-Nijhoff Publishing, 1991.
3. Dubois, D. - Prade, H.: The Handbooks of Fuzzy Sets (Vol. 1-7). Dordrecht : Kluwer Academic Publishers, 2000.
Literature - recommended:
1. Novák, V.: Základy fuzzy modelování. Praha : BEN, 2000.
2. Novák, V.: Fuzzy množiny a jejich aplikace. Praha : SNTL, 1990.
3. Kolesárová, A. - Kováčová, M.: Fuzzy množiny a ich aplikácie. Bratislava : Slovenská technická univerzita v Bratislave, 2004.
4. Talašová, J.: Fuzzy metody ve vícekriteriálním rozhodování a rozhodování. Olomouc : Univerzita Palackého, 2002.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-APM-K combined study --- -- DrEx 0 Recommended course 3 1 W
D-APM-P full-time study --- -- DrEx 0 Recommended course 3 1 W