Lecturer(s)


Talašová Jana, doc. RNDr. CSc.

Holeček Pavel, Mgr. Ph.D.

Course content

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. Level2 fuzzy sets, type2 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.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 39 hours per semester
 Homework for Teaching
 30 hours per semester
 Preparation for the Course Credit
 50 hours per semester

Learning outcomes

To master the mathematical basis of fuzzy sets theory and fuzzy logic, principals of fuzzy and linguistic fuzzy modeling.
Comprehension To understand the mathematical basis of fuzzy sets theory, principals of fuzzy and linguistic fuzzy modeling.

Prerequisites

Fundamentals of the sets theory and algebra.

Assessment methods and criteria

Oral exam, Written 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.

Recommended literature


D. Dubois, H. Prade (Eds.). (2000). Fundamentals of fuzzy sets. Kluwer Academic Publishers, Boston, London, Dordrecht.

G.J. Klir, B. Yuan. (1996). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, New Jersey.

J. Talašová. (2003). Fuzzy metody vícekriteriálního hodnocení a rozhodování. VUP, Olomouc.

V. Novák. (1990). Fuzzy množiny a jejich aplikace. SNTL, Praha.
