|
|
| MATL7870 | Fuzzy Implications | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Gül Deniz ÇAYLI | | Co-Lecturer | Doç. Dr. Ümit Ertuğrul | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to learn fuzzy implications, fuzzy negations, (S,N) and S-implications. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | The students will learn fuzzy implications. | 1,2,3 | 1, | | PO - 2 : | The students will learn negations from fuzzy implications. | 1,2,3 | 1, | | PO - 3 : | The students will learn the laws of contraposition. | 1,2,3 | 1, | | PO - 4 : | The students will learn reciprocal fuzzy implications. | 1,2,3 | 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 | | |
| Definition and basic examples of fuzzy implications, continuity of fuzzy implications, basic properties of fuzzy implications, negations from fuzzy implications, fuzzy negations, natural negations of fuzzy implications, laws of contraposition, reciprocal fuzzy implications, natural negations of t-norms and t-conorms, laws of excluded middle and contradiction, De Morgan triples, (S,N) implications, S-implications. |
| |
| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | An introduction to fuzzy implications | | | Week 2 | Definition of fuzzy implications and some related examples | | | Week 3 | Continuity of fuzzy implications | | | Week 4 | Neutrality property and exchange principle of fuzzy implications and examples | | | Week 5 | Identity principle and ordering property of fuzzy implications and examples | | | Week 6 | Fuzzy negations | | | Week 7 | Natural negations of fuzzy implications | | | Week 8 | Laws of contraposition | | | Week 9 | Mid-term exam | | | Week 10 | Reciprocal fuzzy implications | | | Week 11 | Natural negations of t-norms and t-conorms | | | Week 12 | Laws of excluded middle and contradiction | | | Week 13 | De Morgan triples | | | Week 14 | (S,N) Implications | | | Week 15 | S-Implications | | | Week 16 | End-of-term exam | | | |
| 1 | Baczysnki, M., Jayaram B. 2008; Fuzzy Implications, Studies in Fuzziness and Soft Computing, vol. 231, Springer, Berlin, Heidelberg | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 22/04/2022 | 2 | 30 | | In-term studies (second mid-term exam) | 13 | 13/05/2022 | 2 | 20 | | End-of-term exam | 16 | 09/06/2022 | 2 | 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 | 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 load | | | 225 |
|