Course detail
Mathematical Foundations of Fuzzy Logic
FIT-IMFAcad. year: 2023/2024
At the beginning of the semester, students choose from the supplied topics. On the weekly seminars, they present the topics and discuss them. The final seminar is for assessment of students' performance.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
- Active participation in the exercises (group problem solving, evaluation of the ten exercises): 30 points.
- Projects: group presentation, 70 points.
- Active participation in the exercises (group problem solving, evaluation of the ten exercises): 30 points.
- Projects: group presentation, 70 points.
Aims
Successful students will gain deep knowledge of the selected area of mathematics (depending on the seminar group), and the ability to present the studied area and solve problems within it. The ability to understand advanced mathematical texts, the ability to design nontrivial mathematical proofs.
Study aids
Prerequisites and corequisites
- recommended prerequisite
Mathematical Analysis 1 - recommended prerequisite
Discrete Mathematics
Basic literature
Recommended reading
Classification of course in study plans
Type of course unit
Computer-assisted exercise
Teacher / Lecturer
Syllabus
- From classical logic to fuzzy logic
- Modelling of vague concepts via fuzzy sets
- Basic operations on fuzzy sets
- Principle of extensionality
- Triangular norms, basic notions, algebraic properties
- Triangular norms, constructions, generators
- Triangular conorms, basic notions and properties
- Negation in fuzzy logic
- Implications in fuzzy logic
- Aggregation operators, basic properties
- Aggregation operators, applications
- Fuzzy relations
- Fuzzy preference structures
Project
Teacher / Lecturer
Syllabus
- Triangular norms, class of třída archimedean t-norms
- Triangular norms, construction of continuous t-norms
- Triangular norms, construction of non-continuous t-norms
- Triangular conorms
- Fuzzy negations and their properties
- Implications in fuzzy logic
- Aggregation operators, averaging operators
- Aggregation operators, applications
- Fuzzy relations, similarity, fuzzy equality
- Fuzzy preference structures