Fuzzy Models of Technical Processes and Systems
FSI-9FMSAcad. year: 2020/2021
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.
Learning outcomes of the course unit
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.
Elements of the set theory, algebra and mathematical analysis.
Recommended optional programme components
Recommended or required reading
Klir, G. J. - Yuan B.: Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey : Prentice Hall, 1995. (EN)
Novák, V.: Základy fuzzy modelování. Praha : BEN, 2000.
Novák, V.: Fuzzy množiny a jejich aplikace. Praha : SNTL, 1990.
Zimmermann, H. J.: Fuzzy Sets Theory and Its Applications. Boston : Kluwer-Nijhoff Publishing, 1991. (EN)
Dubois, D. - Prade, H.: The Handbooks of Fuzzy Sets (Vol. 1-7). Dordrecht : Kluwer Academic Publishers, 2000. (EN)
Kolesárová, A. - Kováčová, M.: Fuzzy množiny a ich aplikácie. Bratislava : Slovenská technická univerzita v Bratislave, 2004.
Talašová, J.: Fuzzy metody ve vícekriteriálním rozhodování a rozhodování. Olomouc : Univerzita Palackého, 2002.
Planned learning activities and teaching methods
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.
Language of instruction
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.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is not compulsory, but is recommended.
Type of course unit
20 hours, optionally
Teacher / Lecturer
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.