Türkçe | English FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES Course Catalog http://www.ktu.edu.tr/isbb Phone: +90 0462 +90 (462) 3773112 FENF
FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /    IST4008 Mathematical Analysis of Uncertainty 4+0+0 ECTS:6 Year / Semester Spring Semester Level of Course First Cycle Status Elective Department DEPARTMENT of STATISTICS and COMPUTER SCIENCES Prerequisites and co-requisites None Mode of Delivery Face to face Contact Hours 14 weeks - 4 hours of lectures per week Lecturer Prof. Dr. Türkan ERBAY DALKILIÇ Co-Lecturer ASSOC. PROF. DR. Orhan KESEMEN Language of instruction Turkish Professional practise ( internship ) None The aim of the course: 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.