Course details

Mathematical Foundations of Fuzzy Logic

IMF Acad. year 2016/2017 Winter semester 5 credits

Current academic year

At the beginning of semester, students choose from the supplied topics. On the weekly seminars, they present the topics and discuss about them. The final seminar is for assesment of students' performance.

Guarantor

Hliněná Dana, doc. RNDr., Ph.D. (UMAT)

Language of instruction

Czech, English

Completion

Classified Credit

Time span

  • 26 hrs exercises
  • 26 hrs projects

Assessment points

  • 30 pts numeric exercises
  • 70 pts projects

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

Successfull students will gain deep knowledge of the selected area of mathematics (depending on the seminar group), and 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.

Learning objectives

To extend an area of mathematical knowledge with an emphasis of solution searchings and mathematical problems proofs.

Prerequisite knowledge and skills

Knowledge of "IDA - Discrete Mathematics" and "IMA - Mathematical Analysis" courses.

Study literature

    1. Alsina, C., Frank, M.J., Schweizer, B., Assocative functions: Triangular Norms and Copulas, World Scientific Publishing Company, 2006
    2. Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004

Fundamental literature

    1. Alsina, C., Frank, M.J., Schweizer, B., Assocative functions: Triangular Norms and Copulas, World Scientific Publishing Company, 2006
    2. Baczynski, M., Jayaram, B., Fuzzy implications, Studies in Fuzziness and Soft Computing, Vol. 231, 2008
    3. Carlsson, Ch., Fullér, R., Fuzzy reasoning in decision making and optimization, Studies in Fuzziness and Soft Computing, Vol. 82, 2002
    4. Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004

Syllabus of seminars

Syllabus of numerical exercises:
  1. From classical logic to fuzzy logic
  2. Modelling of vague concepts via fuzzy sets
  3. Basic operations on fuzzy sets
  4. Principle of extensionality
  5. Triangular norms, basic notions, algebraic properties
  6. Triangular norms, constructions, generators
  7. Triangular conorms, basic notions and properties
  8. Negation in fuzzy logic
  9. Implications in fuzzy logic
  10. Aggregation operators, basic properties
  11. Aggregation operators, applications
  12. Fuzzy relations
  13. Fuzzy preference structures

Syllabus - others, projects and individual work of students:
  1. Triangular norms, class of třída archimedean t-norms
  2. Triangular norms, construction of continuous t-norms
  3. Triangular norms, construction of non-continuous t-norms
  4. Triangular conorms
  5. Fuzzy negations and their properties
  6. Implications in fuzzy logic
  7. Aggregation operators, averaging operators
  8. Aggregation operators, applications
  9. Fuzzy relations, similarity, fuzzy equality
  10. Fuzzy preference structures

Syllabus of numerical exercises

  1. From classical logic to fuzzy logic
  2. Modelling of vague concepts via fuzzy sets
  3. Basic operations on fuzzy sets
  4. Principle of extensionality
  5. Triangular norms, basic notions, algebraic properties
  6. Triangular norms, constructions, generators
  7. Triangular conorms, basic notions and properties
  8. Negation in fuzzy logic
  9. Implications in fuzzy logic
  10. Aggregation operators, basic properties
  11. Aggregation operators, applications
  12. Fuzzy relations
  13. Fuzzy preference structures

Progress assessment

Students have to get at least 50 points during the semester.

Controlled instruction

Active participation in the exercises (group problem solving, evaluation of the ten exercises): 30 points.
Projects: group  presentation, 70 points.

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