| Dersin Kodu | Dersin Adı | Dersin Türü | Yıl | Yarıyıl | AKTS | | FMA720 | FUZZY TOPOLOGY | Zorunlu | 1 | 2 | 6 |
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| Dersin Seviyesi |
| Doktora |
| Dersin Amacı |
| The aim of the course is
• to teach L-fuzzy sets
• to equip students with the knowledge and skills of operations of L-fuzzy sets
• to develop the ability of the students to pure maths
• to give students the opportunity to think
• to enable students develop function knowledge
• to allow students become proficient in fuzzy set theory
• to give the students basic information about well fuzzy topology
• to provide the basic knowledge about L-fuzzy compactness
• to introduce the students with L-fuzzy connectedness |
| Dersi Veren Öğretim Görevlisi/Görevlileri |
| Yrd. Doç. Dr. Serkan Karataş |
| Öğrenme Çıktıları |
| 1 | L-bulanık kümeler hakkında bilgi ve beceriye sahip olmak | | 2 | Etkili düşünebilmek | | 3 | L-bulanık kümelerle bulanık kümeler arasındaki ilişkileri açıklayabilmek | | 4 | Teorik (pür) matematik becerisini arttırmak | | 5 | Bulanık topoloji hakkında bilgi sahibi olmak | | 6 | L-bulanık kümeleri üzerinde topolojik yapılar geliştirmek için bireysel ve ekip üyesi olarak sorumluluk almak | | 7 | To have the knowledge and skills of L-fuzzy sets Effectively be able to think Able to explain relations fuzzy sets and L-fuzzy sets Demonstrate the ability to pure mathematics To have knowledge about fuzzy topology Receive responsibilities as an individual and a team member to develop the topological structures on L-fuzzy sets |
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| Öğrenim Türü |
| Formal Education |
| Dersin Ön Koşulu Olan Dersler |
| None |
| Ders İçin Önerilen Diğer Hususlar |
| None |
| Dersin İçeriği |
| • L-fuzzy sets
• L-fuzzy topological space and its fundamental properties
• L-fuzzy continuous functions and the categories of L-fuzzy topological spaces
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| Haftalık Ayrıntılı Ders İçeriği |
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| 1 | Introduction
| | | | 2 | L-fuzzy sets
| | | | 3 | L-fuzzy topological space and its fundamental properties
| | | | 4 | L-fuzzy continuous functions and the categories of L-fuzzy topological spaces
| | | | 5 | L-fuzzy continuous functions and the categories of L-fuzzy topological space
| | | | 6 | The relations among the classical topological spaces, L-topoloical spaces and L-fuzzy topological spaces
| | | | 7 | The relations among the classical topological spaces, L-topoloical spaces and L-fuzzy topological spaces
| | | | 8 | The definition of a base and subbase in L-fuzzy topological spaces, Iiitial and final L-fuzzy topologies
| | | | 9 | Interior and closure operators in L-fuzzy topological spaces
| | | | 10 | Interior and closure operators in L-fuzzy topological spaces
| | | | 11 | Neighborhood systems in L-fuzzy topoogical spaces
| | | | 12 | Neighborhood systems, convergence of nets and filters in L-fuzzy topological spaces
| | | | 13 | Different approximations of compactness in L-fuzzy topological spaces and some of their properties
| | | | 14 | Different approximations of compactness in L-fuzzy topological spaces and some of their properties
| | | | 15 | Uniform L-fuzzy topological spaces
| | | | 16 | Final Exam
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| Ders Kitabı / Malzemesi / Önerilen Kaynaklar |
| 1. Liu Ying-Ming, Fuzzy Topology, World Scientific, 1997
2. N. Palaniappan, Fuzzy Topology, Alpha Science International Ltd., 2002.
3. U. Höhle, S.E.Rodabaugh, Mathematics of Fuzzy Sets; logic, topology and measure theory, The Handbook of Fuzzy Sets Series, Kluwer Academic Publisher, Boston, Dordrecht, London, 1999.
4. S.E.Rodabaugh, E.P.Klement, U. Höhle, Applications of Category Theory to Fuzzy Subsets, Kluwer Academic Publishers, 1992.
5. S.E.Rodabaugh and E.P.Klement, Topological and Algebraic Structures in Fuzzy Sets, A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Kluwer Academic Publishers, 2003.
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| Planlanan Öğrenme Aktiviteleri ve Metodları |
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| Değerlendirme | |
| TOPLAM | 0 | |
| TOPLAM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | TOPLAM | 100 |
| | Dersin Sunulduğu Dil | | | Staj Durumu | | None |
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| İş Yükü Hesaplaması |
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| Midterm Examination | 1 | 2 | 2 |
| Final Examination | 1 | 2 | 2 |
| Makeup Examination | 1 | 2 | 2 |
| Attending Lectures | 10 | 5 | 50 |
| Problem Solving | 10 | 5 | 50 |
| Discussion | 10 | 5 | 50 |
| Self Study | 10 | 5 | 50 |
| Individual Study for Mid term Examination | 10 | 5 | 50 |
| Individual Study for Final Examination | 10 | 5 | 50 |
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| Program ve Öğrenme Çıktıları İlişkisi |
| ÖÇ1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ2 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ6 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | | ÖÇ7 | | | | | | | |
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| * Katkı Düzeyi : 1 Çok düşük 2 Düşük 3 Orta 4 Yüksek 5 Çok yüksek |
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Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
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