# 19D081EFM - Elements of fuzzy mathematics with applications

Course specification
Course title Elements of fuzzy mathematics with applications
Acronym 19D081EFM
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
The goal Introducing students with concepts of fuzzy mathematics, fuzzy sets and fuzzy logic and their applications in fuzzy systems, fuzzy, intuicionistic fuzzy and probabilistic 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 Electrical Engineering.
The outcome Students are capable to apply gained knowledge in further education and practice, to solve mathematical models of fuzzy logic in application to fuzzy systems, 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 sets, fuzzy logic, fuzzy topological spaces. Fuzzy and probabilistic metrics. Sets and functions in fuzzy metric spaces. Characterizations of completeness. Continuity, fuzzy measures and integrals. Fixed points of mappings on fuzzy metric spaces, iterative methods. Convexness in fuzzy metric spaces, applications to optimization problems. Implementation of iterative methods.
Contents of exercises Using computer tools - fuzzy toolbox for Python, for implementation of fuzzy logic. Implementation of iterative methods with Python libraries.
Literature
1. Sinisa Jesic, Theory of functions on fuzzy metric spaces, script, Belgrade 2006, in Serbian
2. Klir J. G., Yuan B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall PTR, New Jersey, USA, 1995
Number of hours per week during the semester/trimester/year
Lectures Exercises OTC Study and Research Other classes
8
Methods of teaching Combination of traditional lectures on blackboard and slides, illustrated with adequate examples from practice and individual work with students on homework and consultations explaining the covered topics. Active analysis of primary scientific sources, organization and conducting numerical experiments and numerical simulations.
Knowledge score (maximum points 100)
Pre obligations Points Final exam Points
Activites during lectures Test paper
Practical lessons 50 Oral examination 50
Projects
Colloquia
Seminars