Course: Fuzzy Sets and their Application 2

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Course title Fuzzy Sets and their Application 2
Course code KMA/FMN2
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Pavlačka Ondřej, RNDr. Ph.D.
  • Stoklasa Jan, Mgr. et Mgr. Ph.D.
  • Talašová Jana, doc. RNDr. CSc.
  • Holeček Pavel, Mgr. Ph.D.
Course content
1. Linguistic variables derived from linguistic scales. 2. Linguistic approximation. Linguistically defined function - fuzzy rule base. 3. Approximate reasoning - Mamdani, Novak and generalized Sugeno algorithms. 4. History of fuzzy controllers. Non-analytic paradigm of control. 5. Schema of fuzzy controller. Design of fuzzy controllers. Example - fuzzy control of inverted pendulum. 6. Analytic input-output functions of Mamdani and Novak fuzzy controllers, Takagi-Sugeno and Sugeno fuzzy controllers. Fuzzy controllers as universal approximators. 7. Application of fuzzy sets in multiple criteria decision making.- overview. 8. Solver of multiple-criteria evaluation tasks - the FuzzME software. Basic structure of mathematical model. Evaluation with respect to quantitative and qualitative criteria. 9. Fuzzy weighted average of partial fuzzy evaluations 10. Evaluation by means of a fuzzy expert system 11. Application of fuzzy sets in decision making under risk. Fuzzy probability space. 12. Fuzzy decision matrices. Fuzzy decision trees.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 30 hours per semester
  • Preparation for the Exam - 60 hours per semester
  • Homework for Teaching - 20 hours per semester
Learning outcomes
To develop knowledge of linguistic fuzzy modeling. To master the following important applications of the fuzzy set theory: fuzzy controllers and fuzzy models of multiple criteria decision making and decision making under risk.
Application Application of the fuzzy sets theory to control (fuzzy controllers), multiple criteria evaluation and decision making and decision making under risk.
Fundamentals of the fuzzy sets theory.
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Assessment methods and criteria
Mark, Oral exam

Credit: written test - student has to prove his/her ability to solve real life problems using the knowledge acquired in this course. Exam: student has to prove knowledge of the theory of fuzzy sets and linguistic fuzzy modeling (fuzzy controllers, fuzzy models of multiple-criteria evaluation and decision making and fuzzy models of decision making under risk) and the ability to apply these models.
Recommended literature
  • C. Von Altrock. (1995). Fuzzy Logic and NeuroFuzzy Applications Explained. Prentice Hall, New Jersey.
  • C. von Altrock. (1996). Fuzzy Logic and NeuroFuzzy Applications in Business and Finance. Prentice Hall, New Yersey.
  • D. Dubois, H. Prade (Eds.). (2000). Fundamentals of fuzzy sets. Kluwer Academic Publishers, Boston, London, Dordrecht.
  • J. J. Buckley. (2004). Fuzzy Statistic. Spinger-Verlag Berlin, Heidelberg.
  • J. Talašová. (2003). Fuzzy metody vícekriteriálního hodnocení a rozhodování. VUP, Olomouc.
  • V. Novák. (1990). Fuzzy množiny a jejich aplikace. SNTL, Praha.
  • Y. J. Lai, C. L. Hwang. (1994). Fuzzy Multiple Objective Decision Making. Springer-Verlag Berlin, Heidelberg.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics and Applications (1) Mathematics courses 3 Summer
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses 1 Summer