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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
Course Catalog
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FBE
GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS / Doctorate
Katalog Ana Sayfa
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MATI7252Triangular norms3+0+0ECTS:7.5
Year / SemesterSpring Semester
Level of CourseThird Cycle
Status Elective
DepartmentDEPARTMENT of MATHEMATICS
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 3 hours of lectures per week
LecturerProf. Dr. Funda KARAÇAL
Co-LecturerDoç.Dr. Ümit Ertuğrul
Language of instruction
Professional practise ( internship ) None
 
The aim of the course:
To give the basic concepts of triangular norms and triangular conforms
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : 1,6,8
PO - 2 : 2,6,8
PO - 3 : 1,2,6,8
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), PO : Learning Outcome

 
Contents of the Course
Triangular norms, triangular conforms and their examples, Continuity, Elementary algebraic properties, semigroups and t-norms, Topological semigroupsand continuous t-norms, lattice ordered monoids and left -continuous t-norms
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Triangular norms, triangular conorms and their examples
 Week 2Continuity
 Week 3Elemantary algebraic properties
 Week 4Elemantary algebraic properties
 Week 5Elemantary algebraic properties
 Week 6Semigroups and t-norms
 Week 7Topological semigroups and continuous t-norms
 Week 8Topological semigroups and continuous t-norms
 Week 9
 Week 10Lattice ordered monoids
 Week 11Lattice ordered monoids
 Week 12Left continuous t-norms
 Week 13Pseudo inverses of monotone functions
 Week 14Pseudo inverses of monotone functions
 Week 15Examples
 Week 16
 
Textbook / Material
1Klement E.P.,Mesiar R., Pap E. , Triangular norms , Kluwer Academic, Dordrecht/Boston/London
 
Recommended Reading
1Hajek .P, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers,Dordrecht/Boston/London
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 11/04/2024 2 30
Quiz 11 25/04/2024 1 30
End-of-term exam 16 7/6/2024 2 40
 
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 3 14 42
Sınıf dışı çalışma 5 14 70
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 4 8 32
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 4 9 36
Proje 0 0 0
Kısa sınav 1 1 1
Dönem sonu sınavı için hazırlık 5 8 40
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load225