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ON THE FUZZIFICATION OF GREEK PLANES OF KLEIN QUADRIC

Yıl 2024, , 300 - 307, 28.06.2024
https://doi.org/10.18038/estubtda.1481317

Öz

A projective space of dimension 3 over a finite Galois field GF(q) is denoted as PG(3,q). It is defined as the set of all one-dimensional subspaces of 4-dimensional vector space over this Galois field. Klein transformation maps a projective plane of PG(3,2) to a Greek plane of the Klein quadric. This paper introduces the fuzzification of Greek planes passing through the base point, any point on the base line different from the base point, and any point not on the base line of the base plane of 5-dimensional fuzzy projective space.

Kaynakça

  • [1] Akça Z, Bayar A, Ekmekçi S, Van Maldeghem H. Fuzzy Projective Spreads of Fuzzy Projective Spaces, Fuzzy Sets and Systems, 2006; 157(24): 3237-3247.
  • [2] Akça Z, Bayar A, Ekmekçi S. On the classification of Fuzzy projective lines of Fuzzy 3-dimensional projective spaces, Communications Mathematics and Statistics, 2007; 55(2): 17-23.
  • [3] Akça Z, Altıntaş A. Fuzzy Counterpart of Klein Quadric, International Electronic Journal of Geometry, 2023; 16(2): 680–688.
  • [4] Bayar A, Akça Z, Ekmekçi S. A Note on Fibered Projective Plane Geometry, Information Science, 2008; 178: 1257-1262.
  • [5] Ekmekçi S, Bayar A, Akça Z. On the classification of Fuzzy projective planes of Fuzzy 3-dimensional projective spaces, Chaos, Solitons and Fractals, 2009; 40: 2146-2151.
  • [6] Hirschfeld JWP. Projective Geometries over Finite Fields, Oxford Mathematical Monographs, 1998.
  • [7] Klein F. Uber die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische, Form Math., 1868; 539-578.
  • [8] Kuijken L, Van Maldeghem H, Kerre E.E, Fuzzy projective geometries from fuzzy vector spaces, in: A. Billot et al. (Eds.), Information Processing and Management of Uncertainty in Knowledge-based Systems, Editions Medicales et Scientifiques, Paris, La Sorbonne, 1998; 1331-1338.
  • [9] Lubczonok P. Fuzzy Vector Spaces, Fuzzy Sets and Systems, 1990; 38: 329-343.
  • [10] Plucker J. On a New Geometry of Space, Philosophical Transactions of the Royal Society of London, 1865; 155: 725-791.
  • [11] Zadeh L. Fuzzy sets, Information control, 1965; 8: 338-353.

ON THE FUZZIFICATION OF GREEK PLANES OF KLEIN QUADRIC

Yıl 2024, , 300 - 307, 28.06.2024
https://doi.org/10.18038/estubtda.1481317

Öz

A projective space of dimension 3 over a finite Galois field GF(q) is denoted as PG(3,q). It is defined as the set of all one-dimensional subspaces of 4-dimensional vector space over this Galois field. Klein transformation maps a projective plane of PG(3,2) to a Greek plane of the Klein quadric. This paper introduces the fuzzification of Greek planes passing through the base point, any point on the base line different from the base point, and any point not on the base line of the base plane of 5-dimensional fuzzy projective space.

Kaynakça

  • [1] Akça Z, Bayar A, Ekmekçi S, Van Maldeghem H. Fuzzy Projective Spreads of Fuzzy Projective Spaces, Fuzzy Sets and Systems, 2006; 157(24): 3237-3247.
  • [2] Akça Z, Bayar A, Ekmekçi S. On the classification of Fuzzy projective lines of Fuzzy 3-dimensional projective spaces, Communications Mathematics and Statistics, 2007; 55(2): 17-23.
  • [3] Akça Z, Altıntaş A. Fuzzy Counterpart of Klein Quadric, International Electronic Journal of Geometry, 2023; 16(2): 680–688.
  • [4] Bayar A, Akça Z, Ekmekçi S. A Note on Fibered Projective Plane Geometry, Information Science, 2008; 178: 1257-1262.
  • [5] Ekmekçi S, Bayar A, Akça Z. On the classification of Fuzzy projective planes of Fuzzy 3-dimensional projective spaces, Chaos, Solitons and Fractals, 2009; 40: 2146-2151.
  • [6] Hirschfeld JWP. Projective Geometries over Finite Fields, Oxford Mathematical Monographs, 1998.
  • [7] Klein F. Uber die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische, Form Math., 1868; 539-578.
  • [8] Kuijken L, Van Maldeghem H, Kerre E.E, Fuzzy projective geometries from fuzzy vector spaces, in: A. Billot et al. (Eds.), Information Processing and Management of Uncertainty in Knowledge-based Systems, Editions Medicales et Scientifiques, Paris, La Sorbonne, 1998; 1331-1338.
  • [9] Lubczonok P. Fuzzy Vector Spaces, Fuzzy Sets and Systems, 1990; 38: 329-343.
  • [10] Plucker J. On a New Geometry of Space, Philosophical Transactions of the Royal Society of London, 1865; 155: 725-791.
  • [11] Zadeh L. Fuzzy sets, Information control, 1965; 8: 338-353.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Sembolik Hesaplama
Bölüm Makaleler
Yazarlar

Münevvere Mine Karakaya 0000-0003-1517-3409

Ziya Akça 0000-0001-6379-0546

Yayımlanma Tarihi 28 Haziran 2024
Gönderilme Tarihi 9 Mayıs 2024
Kabul Tarihi 15 Haziran 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

AMA Karakaya MM, Akça Z. ON THE FUZZIFICATION OF GREEK PLANES OF KLEIN QUADRIC. Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering. Haziran 2024;25(2):300-307. doi:10.18038/estubtda.1481317