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GRADUATE INSTITUTE of NATURAL and APPLIED SCIENCES / DEPARTMENT of MATHEMATICS
Doctorate
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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, Doç. Dr. Gül Deniz Çaylı
Language of instruction
Professional practise ( internship ) None
 
The aim of the course:
This course aims to give the fundamental characteristics of triangular norms and triangular conorms.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : The students will assimilate the concepts of triangular norms and conorms.1,2,31,
PO - 2 : The students will examine the continuity of triangular norms and conorms.1,2,31,
PO - 3 : The students will comprehend the fundamental properties of triangular norms and conorms.1,2,31,
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 conorms) and their examples, continuity, elementary algebraic properties, semigroups and triangular norms, topological semigroups and continuous triangular norms, lattice ordered monoids, left-continuous triangular 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 triangular norms
 Week 7Topological semigroups and continuous triangular norms
 Week 8Topological semigroups and continuous triangular norms
 Week 9Mid-term exam
 Week 10Lattice ordered monoids
 Week 11Lattice ordered monoids
 Week 12Left continuous triangular norms
 Week 13Pseudo inverses of monotone functions
 Week 14Pseudo inverses of monotone functions
 Week 15Examples
 Week 16End-of-term exam
 
Textbook / Material
1Klement, E.P., Mesiar, R., Pap, E. 2000; Triangular Norms,  Kluwer Academic Publishers, Dordrecht
 
Recommended Reading
1Hajek, P. 1998; Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht-Boston-London
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 24/04/2023 2 30
In-term studies (second mid-term exam) 12 15/05/2023 2 20
End-of-term exam 16 12/06/2023 2 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 3 14 42
Sınıf dışı çalışma 3 14 42
Arasınav için hazırlık 10 8 80
Arasınav 2 1 2
Dönem sonu sınavı için hazırlık 9.5 6 57
Dönem sonu sınavı 2 1 2
Total work load225