To convey to students the basic principles of fuzzy logic which are used actively in almost every science and the methods used in mathematical analysis of uncertainty.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

understand the basic concepts of fuzzy logic

1,2,4,5,8,10,11

1

LO - 2 :

consider uncertainty numerically

1,2,4,5,6,8,10,11

1

LO - 3 :

use the fuzzy logic in mathematical analysis of uncertainty

1,2,4,7,9,10,11

1

LO - 4 :

make transactions of fuzzy sets and fuzzy numbers

1,2,4,5,6,10,11

1

LO - 5 :

determine the probability of fuzzy event

1,2,4,5,6,8,9,11

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

System and mathematical model. Concept and types of uncertainty. Uncertainty of the numerical evaluation: Entropy and its properties. Trying stochastic entropy. Conditional entropy. Entropy of complex systems. Entropy of discrete probability distributions. Entropy of absolute continuous distributions. The basic concepts of chaos theory. Modeling of chaotic systems. Using the fuzzy logic in the analysis of mathematical uncertainty : fuzzy logic, fuzzy sets, membership function. Membership function types, α-cut set and level set. Fuzzy set operations. Fuzzy numbers and operations. Fuzzy probability and fuzzy probability of the event. Measurement of fuzziness. Fuzzy probability distributions. Financial market uncertainty and risk reduction methods.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

System and mathematical model. Concept and types of uncertainty.

Week 2

Numerical evaluation of the uncertainty : Entropy and its properties.

Week 3

Entropy of stochastic experiments. Conditional entropy.

Week 4

Entropy of complex systems. Entropy of discrete probability distributions.

Week 5

Entropy of absolute continuous distributions.

Week 6

Using fuzzy logic in mathematical analysis of uncertainty

Week 7

Fuzzy logic, fuzzy sets, membership function.

Week 8

Types of membership function.

Week 9

Mid-term exam

Week 10

Fuzzy set operations.

Week 11

alfa-cut set and level set.

Week 12

Fuzzy numbers and operations.

Week 13

Measurement of fuzziness

Week 14

Fuzzy probability and fuzzy probability of the event.

Week 15

Fuzzy probability distributions.

Week 16

End-of-term exam

Textbook / Material

1

Klir, J. Yuan, B.,1995; Fuzzy sets and fuzzy logic, Prentice Hall PTR, USA.