UIDI008 Fuzzy Approximation Theory

Faculty of Philosophy and Science in Opava
Summer 2015
Extent and Intensity
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
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.
Language of instruction
Czech
Further Comments
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%.
The course is also listed under the following terms Winter 2006, Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, Summer 2011, Winter 2011, Summer 2012, Winter 2012, Summer 2013, Winter 2013, Summer 2014, Winter 2014, Winter 2015, Summer 2016, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Winter 2019, Summer 2020, Winter 2020, Summer 2021, Winter 2021, Summer 2022.
  • Enrolment Statistics (Summer 2015, recent)
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