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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /
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IST4008Mathematical Analysis of Uncertainty4+0+0ECTS:6
Year / SemesterSpring Semester
Level of CourseFirst Cycle
Status Elective
DepartmentDEPARTMENT of STATISTICS and COMPUTER SCIENCES
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Türkan ERBAY DALKILIÇ
Co-LecturerASSOC. PROF. DR. Orhan KESEMEN
Language of instructionTurkish
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 OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : understand the basic concepts of fuzzy logic2,3
LO - 2 : consider uncertainty numerically2,3
LO - 3 : use the fuzzy logic in mathematical analysis of uncertainty2,3
LO - 4 : make transactions of fuzzy sets and fuzzy numbers 2,3
LO - 5 : determine the probability of fuzzy event2,3
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
 WeekSubjectRelated Notes / Files
 Week 1System and mathematical model. Concept and types of uncertainty.
 Week 2Numerical evaluation of the uncertainty : Entropy and its properties.
 Week 3Entropy of stochastic experiments. Conditional entropy.
 Week 4Entropy of complex systems. Entropy of discrete probability distributions.
 Week 5Entropy of absolute continuous distributions.
 Week 6Using fuzzy logic in mathematical analysis of uncertainty
 Week 7Fuzzy logic, fuzzy sets, membership function.
 Week 8Types of membership function.
 Week 9Mid-term exam
 Week 10Fuzzy set operations.
 Week 11alfa-cut set and level set.
 Week 12Fuzzy numbers and operations.
 Week 13Measurement of fuzziness
 Week 14Fuzzy probability and fuzzy probability of the event.
 Week 15Fuzzy probability distributions.
 Week 16End-of-term exam
 
Textbook / Material
1Klir, J. Yuan, B.,1995; Fuzzy sets and fuzzy logic, Prentice Hall PTR, USA.
 
Recommended Reading
1Baykal N., Beyan T., 2004; Bulanık mantık ilke ve temelleri. Bıcaklar kitabevi, Ankara.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 17/04/2022 1 50
End-of-term exam 16 07/06/2022 1 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 4 14 56
Sınıf dışı çalışma 3 14 42
Arasınav için hazırlık 10 1 10
Arasınav 1.5 1 1.5
Dönem sonu sınavı için hazırlık 17 1 17
Dönem sonu sınavı 1.5 1 1.5
Total work load128