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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. 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.
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Learning activities and teaching methods
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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
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Learning outcomes
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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.
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Prerequisites
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Fundamentals of the fuzzy sets theory.
KMA/FMN1Z
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Assessment methods and criteria
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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.
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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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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. Belohlavek, 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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