Course details

Mathematical Foundations of Fuzzy Logic

IMF Acad. year 2024/2025 Winter semester 5 credits

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.

Guarantor

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

Course coordinator

Havlena Vojtěch, Ing., Ph.D. (DITS)

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)

Instructor

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

Learning objectives

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

Recommended prerequisites

Prerequisite knowledge and skills

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

Study literature

  • Carlsson, Ch., Fullér, R., Fuzzy reasoning in decision making and optimization, Studies in Fuzziness and Soft Computing, Vol. 82, 2002.

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

Progress assessment

  • 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.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Thu exercise 1., 2., 3., 4., 5., 6., 8., 9., 10., 11., 12., 13. of lectures A113 08:0009:5064 2BIA 2BIB 3BIT xx Hliněná

Course inclusion in study plans

  • Programme BIT, 2nd year of study, Elective
  • Programme BIT (in English), 2nd year of study, Elective
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