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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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1. Concept of fuzzy set - motivation. Definition of fuzzy set, basic notions. 2. Basic and generalized operations on fuzzy sets. 3. The representation theorem, the extension principle. 4. Characteristics of fuzzy sets. Level-2 fuzzy sets, type-2 fuzzy sets. 5. Fuzzy relation, its separability, composition of fuzzy relations. Binary fuzzy relation on a given set. 6. Fuzzy equivalence, fuzzy compatibility, fuzzy ordering. 7. Fuzzy mappings. Fuzzy numbers, definition, various types of notation, important classes of fuzzy numbers. 8. Special structures of fuzzy numbers - fuzzy scales. 9. Special structures of fuzzy numbers - normalized fuzzy weights. 10. Calculation on fuzzy numbers. Ordering and metrics on fuzzy numbers. 11. Introduction to linguistic fuzzy modeling. 12. Linguistic variable and linguistic scale.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 39 hours per semester
- Homework for Teaching
- 20 hours per semester
- Preparation for the Course Credit
- 30 hours per semester
- Preparation for the Exam
- 60 hours per semester
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Learning outcomes
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Master the basics of fuzzy set theory, fuzzy mathematics and linguistic fuzzy modeling.
Comprehension To understand the mathematical basis of fuzzy sets theory and fuzzy logic, principals of fuzzy and linguistic fuzzy modeling.
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Prerequisites
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Fundamentals of the sets theory and algebra.
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Assessment methods and criteria
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Oral exam
Credit: written test - student has to prove his/her knowledge of the basic concepts of fuzzy set theory and the ability of using them. Exam: student has to prove knowledge of the basics of fuzzy set theory, fuzzy mathematics and linguistic fuzzy modeling.
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Recommended literature
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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 Jersey.
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J. Talašová. (2003). Fuzzy metody vícekriteriálního hodnocení a rozhodování. VUP, Olomouc.
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R. Bělohlávek, J.W. Dauben, G.J. Klir. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press.
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V. Novák. (1990). Fuzzy množiny a jejich aplikace. SNTL, Praha.
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