This paper presents a research study on he images under the Klein mapping of the projectice 3-space order of 4 and the fuzzification of the Klein quadric in 5-dimensional projective space.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Many techniques have been proposed to project the high-dimensional space into a low-dimensional space, one of the most famous methods being principal component analysis.
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Temel Bulgular & Veri:The lines of projective three-space are, via the Klein mapping, in one-to-one correspondence with points of a hyperbolic quadric of the projective 5-space.
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Sonuç & Katkı:This paper presents a research study on he images under the Klein mapping of the projectice 3-space order of 4 and the fuzzification of the Klein quadric in 5-dimensional projective space.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fuzzy point · fuzzy vector space · fuzzy projective space
Abstract
Many techniques have been proposed to project the high-dimensional space into a low-dimensional space, one of the most famous methods being principal component analysis. The Klein quadric is a geometric shape defined by a second-degree homogeneous equation. The lines of projective three-space are, via the Klein mapping, in one-to-one correspondence with points of a hyperbolic quadric of the projective 5-space. This paper presents a research study on he images under the Klein mapping of the projectice 3-space order of 4 and the fuzzification of the Klein quadric in 5-dimensional projective space.
Akça, Z., Altıntaş, A. (2023). Fuzzy Counterpart of Klein Quadric. International Electronic Journal of Geometry, Volume: 16 Issue: 2. https://doi.org/10.36890/iejg.1343784
Akça, Z., Bayar, A., Ekmekçi, S., Van Maldeghem, H.: Fuzzy Projective Spreads of Fuzzy Projective Spaces, Fuzzy Sets and Systems, vol. 157, no. 24, pp. 3237-3247 (2006).
Akça, Z., Bayar, A., Ekmekçi, S.: On the classification of Fuzzy projective lines of Fuzzy 3-dimensional projective spaces, Communications Mathematics and Statistics, Vol. 55(2), 17-23 (2007).
Akça, Z., Bayar, A., Ekmekçi, S., Kaya, R., Thas, J. A., Van Maldeghem H.: Generalized lax Veronesean embeddings of projective spaces, Ars Combin. 103, 65-80 (2012).
Akça, Z.: On fuzzify the notion of Grassmannian in fuzzy n dimensional projective space, International Journal of the Physical Sciences, vol. 6, no. 25, pp. 5877-5882 (2011).
Bayar, A., Akça, Z., Ekmekçi, S.: A Note on Fibered Projective Plane Geometry, Information Science 178, 1257-1262 (2008).
Ekmekçi, S., Bayar, A., Akça, Z.: On the classification of Fuzzy projective planes of Fuzzy 3-dimensional projective spaces, Chaos, Solitons and Fractals 40, 2146-2151 (2009).
Klein, F.: Uber die Transformation der allgemeinen Gleichung des zweiten Grades zwischen Linien-Koordinaten auf eine kanonische, Form Math., p. 539-578 (1868).
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, 1331- 1338 (1998).
Lubczonok P.: Fuzzy Vector Spaces, Fuzzy Sets and Systems 38, 329-343 (1990).
Plucker, J.: On a New Geometry of Space, Philosophical Transactions of the Royal Society of London, Vol. 155, pp. 725-791 (1865).
Zadeh, L.: Fuzzy sets, Information control 8, 338-353 (1965).