Course detail
Fuzzy Sets and Applications
FSI-SFM-AAcad. year: 2024/2025
The course 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, fuzzy probability. It also deals with the applicability of those methods for modelling of vague technical variables and processes, and work with special software of this area.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Attendance at seminars is controlled and the teacher decides on the compensation for absences.
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)
Novák, V.: Fuzzy množiny a jejich aplikace. Praha : SNTL, 1990. (CS)
Zimmermann, H. J.: Fuzzy Sets Theory and Its Applications. Boston : Kluwer-Nijhoff Publishing, 1998. (EN)
Recommended reading
Kolesárová, A. - Kováčová, M.: Fuzzy množiny a ich aplikácie. Bratislava : STU, 2004. (CS)
Novák, V.: Základy fuzzy modelování. Praha : BEN - technická literatura, 2000. (CS)
Talašová, J.: Fuzzy metody ve vícekriteriálním rozhodování a rozhodování. Olomouc : Univerzita Palackého, 2002. (CS)
Elearning
Classification of course in study plans
- Programme N-MAI-A Master's 2 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Operations with fuzzy sets (properties).
3. Operations with fuzzy sets (alfa cuts).
4. Triangular norms and co-norms, complements (properties).
5. Extension principle (Cartesian product, extension mapping).
6. Fuzzy numbers (definition, extension operations, interval arithmetic).7. Fuzzy relations (basic notions, kinds).
8. Fuzzy functions (basic orders, fuzzy parameter, derivation, integral).
9. Linguistic variable (model, fuzzification, defuzzification).
10. Fuzzy logic (multiple value logic, extension).
11. Approximate reasoning and decision-making (fuzzy environment, fuzzy control).
12. Fuzzy probability (basic notions, properties).
13. Fuzzy models design for applications.
Computer-assisted exercise
Teacher / Lecturer
Syllabus
2. Fuzzy sets (basic notions, properties).
3. Operations with fuzzy sets (properties, alfa cuts).
4. Triangular norms and co-norms, complements.
5. Extension principle of mapping.
6. Fuzzy numbers (extension unary and binary operations).
7. Fuzzy numbers and interval arithmetic.
8. Fuzzy relations (orders, operations).
9. Fuzzy functions with fuzzy parameter (derivation, integral).
10. Linguistic variable (operators, presentation).
11. Fuzzy logic (operations, properties).
12. Approximate reasoning and decision-making (fuzzy control).
13. Applications of fuzzy models.
Elearning