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| MATI7253 | Aggregation Functions | 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 | Other lecturers | | Language of instruction | | | Professional practise ( internship ) | None | | | | The aim of the course: | | Major aim of the course is to investigate aggregation functions and to give detailed knowledge about this subject. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | Knows the definiton of aggregation functions | 1,2,3,8 | 1, | | PO - 2 : | Knows different classes of aggregation functions | 1,2,3,8 | 1, | | PO - 3 : | Finds genrators of the sub-class of aggregation functions | 1,2,3,8 | 1, | | PO - 4 : | Constructs new aggregation functions on some sub-classes of aggregation functions. | 1,2,3,8 | 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 | | |
| Main Motivations and Scope; Basic definitions and examples; Conventional Notation; Elementary Mathematical Properties; Grouping-Based properties; İnvariance Properties; Conjunctive and Disjunctive Aggregation Functions; Generated Conjunctive Aggregation Functions; Triangular Norms and Related Conjunctive Aggregation Functions; Copulas and Quasi Copulas;Disjunctive Aggregation Functions; Uninorms; Nullnorms; More Aggregation Functions related to T-norms;Restricted Distributivity |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Main Motivations and Scope | | | Week 2 | Basic definitions and examples | | | Week 3 | Conventional Notation | | | Week 4 | Elementary Mathematical Properties | | | Week 5 | Grouping-Based properties | | | Week 6 | Invariance Properties | | | Week 7 | Conjunctive and Disjunctive Aggregation Functions | | | Week 8 | Generated Conjunctive Aggregation Functions | | | Week 9 | Midterm | | | Week 10 | Triangular Norms and Related Conjunctive Aggregation Functions | | | Week 11 | Copulas and Quasi Copulas | | | Week 12 | Disjunctive Aggregation Functions | | | Week 13 | Uninorms | | | Week 14 | Nullnorms | | | Week 15 | More Aggregation Functions related to T-norms, Restricted Distributivity | | | Week 16 | Final Exam | | | |
| 1 | Grabisch, M.; Marichal; J-L., Mesiar, R.; Pap, E. 2009; Aggregation Functions, Cambridge University Press. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9. hafta | 04.2025 | 90 | 50 | | End-of-term exam | 16. hafta | 06.2025 | 120 | 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 | | Arasınav | 1.5 | 1 | 1.5 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 45.5 |
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