Course detail

Mathematical Foundations of Fuzzy Logic

FIT-IMFAcad. year: 2017/2018

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.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Dana Hliněná, Ph.D.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

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.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

    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

Work placements

Not applicable.

Aims

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

Specification of controlled education, way of implementation and compensation for absences

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Basic literature

Alsina, C., Frank, M.J., Schweizer, B., Assocative functions: Triangular Norms and Copulas, World Scientific Publishing Company, 2006Baczynski, 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, 2002Kolesárová, A., Kováčová, M., Fuzzy množiny a ich aplikácie, STU v Bratislave, 2004

Recommended reading

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

Classification of course in study plans

  • Programme IT-BC-3 Bachelor's

    branch BIT , 2 year of study, winter semester, elective

Type of course unit

 

Fundamentals seminar

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Dana Hliněná, Ph.D.

Syllabus

  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

Project

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Dana Hliněná, Ph.D.