Course detail
Mathematical Foundations of Fuzzy Logic
FIT-IMFAcad. year: 2021/2022
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
Learning outcomes of the course unit
The ability to understand advanced mathematical texts, the ability to design nontrivial mathematical proofs.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Projects: group presentation, 70 points.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Projects: group presentation, 70 points.
Recommended optional programme components
Prerequisites and corequisites
- recommended prerequisite
Mathematical Analysis 1 - recommended prerequisite
Discrete Mathematics
Basic literature
Recommended reading
Baczynski, M., Jayaram, B., Fuzzy implications, Studies in Fuzziness and Soft Computing, Vol. 231, 2008.
Carlsson, Ch., Fullér, R., Fuzzy reasoning in decision making and optimization, Studies in Fuzziness and Soft Computing, Vol. 82, 2002.
Carlsson, Ch., Fullér, R., Fuzzy reasoning in decision making and optimization, Studies in Fuzziness and Soft Computing, Vol. 82, 2002.
Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004.
Trillas, E., Eciolaza, L, Fuzzy logic-An introductory course for engineering students, Studies in Fuzziness and Soft Computing, 2015.
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