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
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Attendance at lectures is not compulsory, but is recommended.
Aims
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
Prerequisites and corequisites
Basic literature
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
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
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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.