# 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
1. S. Jesic, Theory of functions on Fuzzy metric spaces, script, Belgrade 2006.
2. Chaos, Solitons and Fractals, scientific journal on SCI list, following current scientific articles
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