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Course detail

Fuzzy Models of Technical Processes and Systems

Course unit code: FSI-9FMS
Academic year: 2016/2017
Year of study: Not applicable.
Semester: winter
Number of ECTS credits:
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.
Mode of delivery:
Not applicable.
Elements of the set theory, algebra and mathematical analysis.
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
Klir, G. J. - Yuan B.: Fuzzy Sets and Fuzzy Logic - Theory and Applications. New Jersey : Prentice Hall, 1995.
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.
Dubois, D. - Prade, H.: The Handbooks of Fuzzy Sets (Vol. 1-7). Dordrecht : Kluwer Academic Publishers, 2000.
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:
Czech, English
Work placements:
Not applicable.
Course curriculum:
Not applicable.
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:

Lecture: 20 hours, optionally
Teacher / Lecturer: doc. RNDr. Zdeněk Karpíšek, CSc.
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.

The study programmes with the given course