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Lecturer(s)
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Krupka Michal, doc. RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming), Work with Text (with Book, Textbook)
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Learning outcomes
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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.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam
Completing the assignments. Passing the exam.
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Recommended literature
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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).
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Gottwald S. (2001). A Treatise on Many-Valued Logics. Taylor & Francis Group.
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Klir G. J., Yuan B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall.
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Nguyen H. T., Walker E. A. (2005). A First Course in Fuzzy Logic. Chapman & Hall/CRC; 3 edition.
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Radim Bělohlávek, Joseph W. Dauben, George J. Klir. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford.
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