Course: Fuzzy Sets and their Applications

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Course title Fuzzy Sets and their Applications
Course code KMI/PGSFM
Organizational form of instruction Lecture
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 12
Language of instruction Czech, English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Talašová Jana, doc. RNDr. CSc.
  • Krupka Michal, doc. RNDr. Ph.D.
Course content
The course provides an overview of the theory and applications of fuzzy sets. 1. Structures of truth degrees, logical connectives in fuzzy logic, t-norms, residuated lattices, aggregation operators. 2. Fuzzy sets, fuzzy relations, operations with fuzzy sets and fuzzy relations, generalized fuzzy sets. Basic types of fuzzy relations on a set. 3. Fuzzy relational equations. 4. Fuzzification, intuitive approach, fuzzy logic approach, basic requirements. Extension principle. 5. Rule-based systems and fuzzy controllers, inference, fuzzification and defuzzification, universal approximation property. 6. Fuzzy clustering, basic approaches. 7. Fuzzy sets and databases, relational model of data over domains with similarities. 8. Fuzzy automata, fuzzy languages.

Learning activities and teaching methods
Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
Learning outcomes
To master the basis of fuzzy set theory and selected applications
1. Knowledge Describe and understand comprehensively principles and methods of theory of fuzzy sets.

Assessment methods and criteria
Oral exam

Recommended literature
  • Bělohlávek R. (2002). Fuzzy Relational Systems: Foundations and Principles. NY: Kluwer Academic/Plenum Press (Vol.20 of IFSR Int. Series on Systems Science and Engineering).
  • Gottwald S. (2001). A Treatise on Many-Valued Logics. Taylor & Francis Group.
  • Klir G. J., Yuan B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall.
  • Nguyen H. T., Walker E. A. (2005). A First Course in Fuzzy Logic. Chapman & Hall/CRC; 3 edition.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester