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| MATL7243 | Soft Sets and Soft Algebraic Structures | 3+0+0 | ECTS:7.5 | | Year / Semester | Fall Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Sultan YAMAK | | Co-Lecturer | Assoc. Prof. Dr. Osman Kazancı | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | In this Course we study Molodtsov notion of soft sets and fuzzy soft sets considering the fact that the parameters are mostly fuzzy hedges or fuzzy parameters. We discuss soft algebraic structure and give the definition of fuzzy soft algebraic structure. We define operations on fuzzy soft algebraic structure and prove some results on them. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | define the concept of soft sets | 1,4 | 1 | | PO - 2 : | know some applications of soft sets | 1,4 | 1 | | PO - 3 : | identify soft algebraic structures | 1,4 | 1 | | PO - 4 : | identify fuzzy soft algebraic structures | 1,4 | 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), PO : Learning Outcome | | |
| Soft sets, soft groups, soft subgroups, soft homomorphism, soft rings, soft subrings, modules, soft submodules, fuzzy soft sets, fuzzy soft groups, fuzzy soft subgroups. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Soft sets | | | Week 2 | soft groups | | | Week 3 | soft subgroups | | | Week 4 | soft homomorphism | | | Week 5 | soft rings | | | Week 6 | soft subrings | | | Week 7 | soft modules | | | Week 8 | Mid-term exam | | | Week 9 | soft submodules | | | Week 10 | fuzzy soft sets | | | Week 11 | fuzzy soft groups | | | Week 12 | fuzzy soft subgroups | | | Week 14 | fuzzy soft modules | | | Week 15 | fuzzy soft submodules | | | Week 16 | End-of-term exam | | | |
| 1 | D. Molodsov 1999, Soft set theory, First results, Computers & Mathematics with Applications 37 19-31. | | | 2 | H. Aktaş, N. Çağman 2007, Soft sets and soft group, Information Science 177 2726-2735. | | | |
| 1 | P.K. Maji, R. Biswas, A.R. Roy 2003, Soft set theory, Computers & Mathematics with Applications 45 555-562. | | | 2 | P.K. Maji, R. Biswas, A.R. Roy 2001, Fuzzy soft sets, Journal of Fuzzy Mathematics 9 (3) 589-602. | | | 3 | Aygünoğlu A., Aygün A. 2009, Introduction to fuzzy soft groups, Computers and Mathematics with Applications 58 1279-1286 | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 27/11/2023 | 2,00 | 20 | | In-term studies (second mid-term exam) | 12 | 26/12/2023 | 2,00 | 30 | | End-of-term exam | 17 | 16/01/2024 | 2,00 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 8 | 14 | 112 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 2 | 2 | 4 | | Ödev | 10 | 1 | 10 | | Dönem sonu sınavı için hazırlık | 16 | 1 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 201 |
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