FPF:UIDI008 Fuzzy Approximation Theory - Course Information
UIDI008 Fuzzy Approximation Theory
Faculty of Philosophy and Science in OpavaSummer 2022
- Extent and Intensity
- 0/0/0. 0 credit(s). Type of Completion: dzk.
- Guaranteed by
- Profesor Irina Perfilieva, CSc.
Institute of Computer Science – Faculty of Philosophy and Science in Opava - Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Autonomous Systems (programme FPF, P1801 Inf) (2)
- Autonomous Systems (programme FPF, P1801 Inf) (2)
- Course objectives
- The objective of the course is to introduce the elements of the fuzzy approximation theory. The selection of particular themes will be harmonized with the topic of the PhD thesis of the student.
- Syllabus
- 1. Approximation spaces and quality of approximation. Approximation of continuous function of fuzzy relations.
2. The universal approximation theorem. The theorem on the best approximation of continuous function of fuzzy relations.
3. Representation of monotone function by fuzzy relation and de-fuzzyfication LOM.
4. Fuzzy function, its representation, interpolation and approximation of fuzzy relations. Fuzzy similarity and its examples.
5. Extensionality of functions. Theorem on representation of extensional function by normal forms.
6. Discrete normal forms and approximation of extensional function by discrete normal forms, approximation error estimation.
7. Representation of continuous and piecewise monotone function by discrete normal forms.
8. Additive normal forms and their approximation properties.
9. Fuzzy decomposition of universe by basic functions.
10. The F-transformation, an estimation of its components. Reverse F-transformation and the uniform convergence theorem.
11. Generalized Euler method for solution of the Cauchy problem.
- 1. Approximation spaces and quality of approximation. Approximation of continuous function of fuzzy relations.
- Teaching methods
- Interactive lecture
Lecture with a video analysis - Assessment methods
- Exam
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Teacher's information
- A literature review of selected topics of fuzzy approximation theory due to the teacher's selection related to the PhD thesis of the student. An oral exam - minimum success rate 50%.
- Enrolment Statistics (recent)
- Permalink: https://is.slu.cz/course/fpf/summer2022/UIDI008