Öz
Kaynakça
- L. A. Zadeh, Fuzzy Sets, Information and Control 8 (3) (1965) 338--353.
- J. Goguen, $\mathcal{L}$-Fuzzy Sets, Journal of Mathematical Analysis and Applications 18 (1) (1967) 145--174.
- G. D. Birkhoff, Lattice Theory, 3rd Edition, American Mathematical Society, New York, 1973.
- K. Menger, Statistical Metrics, Proceedings of the National Academy of Sciences 28 (12) (1942) 535--537.
- B. Schweizer, A. Sklar, Statistical Metric Spaces, Pacific Journal of Mathematics 10 (1) (1960) 313--334.
- B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Dover Publications, New York, 2011.
- I. Kramosil, J. Michalek, Fuzzy Metrics and Statistical Metric Spaces, Kybernetica 11 (5) (1975) 336--344.
- A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets and Systems 64 (3) (1994) 395--399.
- V. Gregori, S. Morillas, A. Sapena, Examples of Fuzzy Metrics and Applications, Fuzzy Sets and Systems 170 (1) (2011) 95--111.
- R. Saadati, A. Razani, H. Adibi, A Common Fixed Point Theorem in $\mathcal{L}$-Fuzzy Metric Spaces, Chaos, Solitons $\&$ Fractals 33 (2) (2007) 358--363.
- S. Morillas, V. Gregori, G. Peris-Fajarnes, P. Latorre, A Fast Impulsive Noise Color Image Filter Using Fuzzy Metrics, Real-Time Imaging 11 (5-6) (2005) 417--428.
- C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag Berlin, Heidelberg, 1999.
- C. D. Aliprantis, O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.
- C. Çevik, I. Altun, Vector Metric Spaces and Some Properties, Topological Methods in Nonlinear Analysis 34 (2) (2009) 375--382.
- Ş. Eminoğlu, C. Çevik, Fuzzy Vector Metric Spaces and Some Results, Journal of Nonlinear Sciences and Applications 10 (2017) 3429--3436.
Öz
This paper contributes to the broader studies of fuzzy vector metric spaces and fuzzy metric spaces based on order structures beyond the unit interval. It defines the notions of the left (right) order convergence and continuity in non-Arcimedean $\mathcal{L}$-fuzzy vector metric spaces. The notation $\mathcal{M}_E(a,b,s)$ means the nearness between $a$ and $b$ according to any positive vector $s$. This study exemplifies definitions and reaches some well-known results. Moreover, it proposes the concept of $\mathcal{L}$-fuzzy vector metric diameter and studies some of its basic properties. Further, the present paper proves the Cantor intersection theorem and the Baire category theorem via these concepts. Finally, this study discusses the need for further research.
Anahtar Kelimeler
Non-Archimedean $\mathcal{L}$-fuzzy vector metrics left and right order convergence $\mathcal{L}$-fuzzy vector diameter Riesz spaces
Kaynakça
- L. A. Zadeh, Fuzzy Sets, Information and Control 8 (3) (1965) 338--353.
- J. Goguen, $\mathcal{L}$-Fuzzy Sets, Journal of Mathematical Analysis and Applications 18 (1) (1967) 145--174.
- G. D. Birkhoff, Lattice Theory, 3rd Edition, American Mathematical Society, New York, 1973.
- K. Menger, Statistical Metrics, Proceedings of the National Academy of Sciences 28 (12) (1942) 535--537.
- B. Schweizer, A. Sklar, Statistical Metric Spaces, Pacific Journal of Mathematics 10 (1) (1960) 313--334.
- B. Schweizer, A. Sklar, Probabilistic Metric Spaces, Dover Publications, New York, 2011.
- I. Kramosil, J. Michalek, Fuzzy Metrics and Statistical Metric Spaces, Kybernetica 11 (5) (1975) 336--344.
- A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets and Systems 64 (3) (1994) 395--399.
- V. Gregori, S. Morillas, A. Sapena, Examples of Fuzzy Metrics and Applications, Fuzzy Sets and Systems 170 (1) (2011) 95--111.
- R. Saadati, A. Razani, H. Adibi, A Common Fixed Point Theorem in $\mathcal{L}$-Fuzzy Metric Spaces, Chaos, Solitons $\&$ Fractals 33 (2) (2007) 358--363.
- S. Morillas, V. Gregori, G. Peris-Fajarnes, P. Latorre, A Fast Impulsive Noise Color Image Filter Using Fuzzy Metrics, Real-Time Imaging 11 (5-6) (2005) 417--428.
- C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, Springer-Verlag Berlin, Heidelberg, 1999.
- C. D. Aliprantis, O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.
- C. Çevik, I. Altun, Vector Metric Spaces and Some Properties, Topological Methods in Nonlinear Analysis 34 (2) (2009) 375--382.
- Ş. Eminoğlu, C. Çevik, Fuzzy Vector Metric Spaces and Some Results, Journal of Nonlinear Sciences and Applications 10 (2017) 3429--3436.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Operatör Cebirleri ve Fonksiyonel Analiz |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 30 Aralık 2023 |
| Yayımlanma Tarihi | 31 Aralık 2023 |
| Gönderilme Tarihi | 29 Ağustos 2023 |
| Yayımlandığı Sayı | Yıl 2023 Sayı: 45 |
Kaynak Göster
- Makale Dosyaları