Mathematics 6F

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Random vector. Function of a random vector. Multidimensional normal distribution. Random choice, dispersion, statistics. Point estimates of parameters. Maximum likelihood method. Interval of reliability. Hypotheses testing. Linear regression. Basics of correlation analysis. Fuzzy sets. Basic notions. Representation by alpha-cuts. Fuzzy negations. Fuzzy intersections and unions. Fuzzy proposition calculus. Fuzzy implications. Aggregation operators. Extension principle. Fuzzy relations. Applications of fuzzy logic in control, defuzzification. Alternative approches, general types of fuzzy sets, quantum logics.

Requirements:

Linear Algebra, Calculus, Discrete Mathematics

Syllabus of lectures:

1. Random vector. Function of a random vector

2. Multidimensional normal distribution

3. Random choice, dispersion, statistics

4. Point estimates of parameters

5. Maximum likelihood method

6. Interval of reliability. Hypotheses testing

7. Linear regression. Basics of correlation analysis

8. Fuzzy sets. Basic notions

9. Representation by alpha-cuts. Fuzzy negations

10. Fuzzy intersections and unions. Fuzzy propositional calculus

11. Fuzzy implications. Aggregation operators

12. Extension principle. Fuzzy relations

13. Applications of fuzzy logic in control, defuzzification

14. Alternative approaches, general types of fuzzy sets, quantum logics

Syllabus of tutorials:

1. Random vector. Function of a random vector

2. Multidimensional normal distribution

3. Random choice, dispersion, statistics

4. Point estimates of parameters

5. Maximum likelihood method

6. Interval of reliability. Hypotheses testing

7. Linear regression. Basics of correlation analysis

8. Fuzzy sets. Basic notions

9. Representation by alpha-cuts. Fuzzy negations

10. Fuzzy intersections and unions. Fuzzy propositional calculus

11. Fuzzy implications. Aggregation operators

12. Extension principle. Fuzzy relations

13. Applications of fuzzy logic in control, defuzzification

14. Alternative approaches, general types of fuzzy sets, quantum logics

Study Objective:

Basic principles mathematical statistics and fuzzy logic.

Study materials:

[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.

[2] Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. 3rd ed., McGraw-Hill, 1974.

[3] Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. 2nd ed., Chapman & Hall/CRC, Boca Raton/London/New York/Washington, 2000.

[4] Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications.

Prentice-Hall, 1995.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: