DS2TF - Theory of Functions on Fuzzy Metric Spaces
| Course specification | ||||
|---|---|---|---|---|
| Course title | Theory of Functions on Fuzzy Metric Spaces | |||
| Acronym | DS2TF | |||
| Study programme | Electrical Engineering and Computing | |||
| Module | ||||
| Type of study | doctoral studies | |||
| Lecturer (for classes) | ||||
| Lecturer/Associate (for practice) | ||||
| Lecturer/Associate (for OTC) | ||||
| ESPB | 9.0 | Status | elective | |
| Condition | Knowledge of classical mathematical analysis, notion of metric spaces and function theory | |||
| The goal | Introducing students with spaces with non-deterministic distances, especially with fuzzy metric and intuicionistic fuzzy metric spaces, their structure, properties of mappings on these spaces and applications of functional analysis on spaces with fuzzy structure in optimization problems, iteration methods and applications in electrotechnics and computer science. | |||
| The outcome | Students are capable to form iterative methods as optimal for solving various types of equations that come out of actual problems in physics, electrical engineering and other sciences and have non-deterministic (parametric) definitions. | |||
| Contents | ||||
| Contents of lectures | Fuzzy and intuicionistic fuzzy metrics. Completeness, precompactness, compactness of sets in fuzzy metric spaces. Characterizations of completeness. Continuity and uniform continuity of functions. Fixed points of mappings on fuzzy metric spaces and iterative methods. Convexness in fuzzy metric spaces and applications to optimization problems. Applications in electrotechnics. | |||
| Contents of exercises | Implementation of iterative methods using mathematical software. | |||
| Literature | ||||
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| Number of hours per week during the semester/trimester/year | ||||
| Lectures | Exercises | OTC | Study and Research | Other classes |
| 6 | ||||
| Methods of teaching | Combination of traditional presentation on blackboard, slides, communication of students through internet and individual work with students while working on home work and explanation of current topics. Discussion about home work during semester, colloquium at the end of semester. | |||
| Knowledge score (maximum points 100) | ||||
| Pre obligations | Points | Final exam | Points | |
| Activites during lectures | 0 | Test paper | 50 | |
| Practical lessons | 0 | Oral examination | 20 | |
| Projects | 0 | |||
| Colloquia | 30 | |||
| Seminars | 0 | |||