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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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MATL7241THE LATTİCES of FUZZY SUBALGEBRAS3+0+0ECTS:7.5
Year / SemesterFall 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. Sultan YAMAK
Co-LecturerProf. Dr. Gül Deniz ÇAYLI
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
To refine the lattices of fuzzy subalgebraic structure and to characterize classical algebraic structures.
 
Programme OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
PO - 1 : Understand fuzzy subalgebraic structures1 - 31,3,
PO - 2 : Axamine the lattices of fuzzy subalgebraic structures1 - 41,3
PO - 3 : Determinates classical algebraic structures1 - 41,3
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), PO : Learning Outcome

 
Contents of the Course
Lattice of the subgroups and normal subgroups; lattices subrings and ideals; lattices of submodules; lattices of fuzzy subgroups; lattices of fuzzy subrings and ideals; lattices of fuzzy submodules.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Algebraic Structures and sublattices of algebraic structures
 Week 2Fuzzy subalgebraic structures
 Week 3the lattices of fuzzy subgroups and fuzzy normal subgroups
 Week 4the lattices of fuzzy subgroups and fuzzy normal subgroups
 Week 5the lattices of fuzzy subgroups and fuzzy normal subgroups
 Week 6the lattices of fuzzy subrings and fuzzy ideals
 Week 7the lattices of fuzzy subrings and fuzzy ideals
 Week 8the lattices of fuzzy subrings and fuzzy ideals
 Week 9Midterm
 Week 10the lattices of fuzzy submodules
 Week 11the lattices of fuzzy submodules
 Week 12the lattices of fuzzy submodules
 Week 13Homomorphis of fuzzy groups
 Week 14Applications
 Week 15Applications
 Week 16Final exam
 
Textbook / Material
1J.N. Mordeson, D.S. Malik, Fuzzy Commutative Algebra, World Scientific Publishing, London, 1998
 
Recommended Reading
1T.H. Hungerford, Algebra, Springer, New York, 1974.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 8 18/04/2025 2 30
In-term studies (second mid-term exam) 11 10/05/2025 2 20
End-of-term exam 16 07/06/2026 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 7 14 98
Arasınav için hazırlık 8 1 8
Arasınav 2 1 2
Ödev 1 14 14
Kısa sınav 2 1 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Total work load178