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Lecturer(s)
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Pavlačka Ondřej, RNDr. Ph.D.
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Course content
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Fuzzy sets theory as an instrument of the mathematical modeling of vagueness. Definition of fuzzy set, mathematical structures of membership degrees. Operations on fuzzy sets. T-norms, T-conorms, negations, implications. Aggregating operators - averaging, Sugeno and Choquet integral. Representation theorem, extension principle. Fuzzy relations, fuzzy equivalence, fuzzy compatibility, fuzzy ordering. Fuzzy mappings. Fuzzy numbers, important classes of fuzzy numbers. Calculation on fuzzy numbers. Ordering and metrics on fuzzy numbers. Linguistic variables, special structures of values of linguistic variables. Linguistic functions - rule bases. Approximate reasoning. Linguistic approximation. Fuzzy controllers. History of fuzzy controllers. Principle of fuzzy controller. Design of fuzzy controller. Mamdani, Takagi - Sugeno and Sugeno fuzzy controllers. Fuzzy controllers as universal approximators. Applications of fuzzy sets in multiple criteria decision making. Objective-oriented approach to evaluation and its connection with the fuzzy sets paradigm. Fuzzy Weighted Average Method, Fuzzy Expert System Method. Applications of fuzzy sets in decision making under risk. Fuzzy probabilities. Fuzzy decision matrices. Fuzzy decision trees.
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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 fuzzy set theory and its applications particularly in fuzzy control and multiple criteria evaluation
Understanding To understand the fuzzy set theory and its applications particularly in fuzzy control and multiple criteria evaluation.
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Prerequisites
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Master's degree in mathematics.
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Assessment methods and criteria
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Oral exam
Exam: to know and to understand the subject
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Recommended literature
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C. von Altrock. (1995). Fuzzy Logic and NeuroFuzzy Applications Explained. Prentice Hall, New Jersey.
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C. von Altrock. (1996). Fuzzy Logic and NeuroFuzzy Applications in Business and Finance. Prentice Hall, New Yersey.
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D. Dubois, H. Prade (Eds.). (2000). Fundamentals of fuzzy sets. Kluwer Academic Publishers, Boston, London, Dordrecht.
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G. J. Klir, B. Yuan. (1996). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, New Yersey.
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H. Rommelfanger. (1988). Fuzzy Decision Support Systeme. Springer - Verlag, Berlin, Heidelberg.
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H. Rommelfanger, S. Eickemeier. (2002). Entscheidungstheorie. Springer - Verlag, Berlin, Heidelberg.
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J. Ramík, M. Vlach. (2001). General Concavity in Fuzzy Optimization and Decision Analysis. Kluwer, Academic Publishers, Boston-Dordrecht-London.
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J. Talašová. (2003). Fuzzy metody vícekriteriálního hodnocení a rozhodování. VUP, Olomouc.
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J.J. Buckley. (2004). Fuzzy Statistic. Spinger-Verlag, Berlin, Heidelberg.
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R. Viertl. (1996). Statistical Methods for Non-Precise Data. CRC Press, Boca Raton, Florida.
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V. Novák. (1990). Fuzzy množiny a jejich aplikace. SNTL, Praha.
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Y. J. Lai, C. L., Hwang. (1994). Fuzzy Multiple Objective Decision Making. Springer - Verlag, Berlin, Heidelberg.
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