Araştırma Makalesi
BibTex RIS Kaynak Göster

Fuzzy Collineations of Fuzzy Projective Planes

Yıl 2022, Cilt: 10 Sayı: 1, 166 - 170, 15.04.2022

Öz

In this paper, the fuzzy counterparts of the collineations defined in the classical projective planes are defined in fuzzy projective planes. The properties of fuzzy projective plane left invariant under the fuzzy collineations are characterized depending on the base point, base line and the membership degrees of fuzzy projective plane.

Kaynakça

  • [1] K.S. Abdukhalikov, The Dual of a Fuzzy Subspace, Fuzzy Sets and Systems, 7, 375-381, 1996.
  • [2] E. Altintas, On Maps in Fuzzy and Intuitionistic Fuzzy Projective Planes, Eskis¸ehir Osmangazi University, Institute of Science, Doctoral Thesis, 2020.
  • [3] Z. Akc¸a, A. Bayar and S. Ekmekc¸i, Fuzzy projective spreads of fuzzy projective spaces, Fuzzy Sets and Systems, 157, 3237-3247, 2006.
  • [4] F. Buekenhout, Handbook of Incidence Geometry, Building and Foundations, North- Holland, Amsterdam, 1995.
  • [5] H. S. M. Coxeter, Projective Geometry, Springer- Verlag, 1974.
  • [6] S. Ekmekc¸i, Z. Akc¸a and A. Bayar, On the classification of fuzzy projective planes of fuzzy 3 dimensional projective space, Chaos, Solitons and Fractals, 40 (5), 2146–2151, 2009.
  • [7] D. R. Hughes and F. C. Piper, Projective Planes, Springer-Verlag, New York Heidelberg Berlin, 1973.
  • [8] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal of Mathematical Analysis and Applications, 58 (1), 135-146, 1977.
  • [9] L. Kuijken, H.V. Maldeghem and E.E. Kerre, Fuzzy projective geometries from fuzzy vector spaces, Information processing and management of uncertainty in knowledge-based systems. Editions Medicales et Scientifiques. Paris,La Sorbonne, 1331–1338, 1998.
  • [10] L. Kuijken, H.V. Maldeghem and E.E. Kerre, Fuzzy projective geometries from fuzzy groups, Tatra Mountains Mathematical Publications, 16, 85-108, 1999.
  • [11] L. Kuijken, Fuzzy projective geometries, Mathematics, Computer Science, EUSFLAT-ESTYLF Joint Conf., 1999.
  • [12] L. Kuijken and H.V. Maldeghem, Fibered geometries, Discrete Mathematics, 255, 259-274, 2002.
  • [13] L. Kuijken and H.V. Maldeghem, On the definition and some conjectures of fuzzy projective planes by Gupta and Ray, and a new definition of fuzzy building geometries, Fuzzy Sets and Systems, 138, 667-685, 2003.
  • [14] A. Rosenfeld, Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35, 512-517, 1971.
  • [15] L.A. Zadeh, Fuzzy sets, Information and Control, 8, 338-353, 1965.
Yıl 2022, Cilt: 10 Sayı: 1, 166 - 170, 15.04.2022

Öz

Kaynakça

  • [1] K.S. Abdukhalikov, The Dual of a Fuzzy Subspace, Fuzzy Sets and Systems, 7, 375-381, 1996.
  • [2] E. Altintas, On Maps in Fuzzy and Intuitionistic Fuzzy Projective Planes, Eskis¸ehir Osmangazi University, Institute of Science, Doctoral Thesis, 2020.
  • [3] Z. Akc¸a, A. Bayar and S. Ekmekc¸i, Fuzzy projective spreads of fuzzy projective spaces, Fuzzy Sets and Systems, 157, 3237-3247, 2006.
  • [4] F. Buekenhout, Handbook of Incidence Geometry, Building and Foundations, North- Holland, Amsterdam, 1995.
  • [5] H. S. M. Coxeter, Projective Geometry, Springer- Verlag, 1974.
  • [6] S. Ekmekc¸i, Z. Akc¸a and A. Bayar, On the classification of fuzzy projective planes of fuzzy 3 dimensional projective space, Chaos, Solitons and Fractals, 40 (5), 2146–2151, 2009.
  • [7] D. R. Hughes and F. C. Piper, Projective Planes, Springer-Verlag, New York Heidelberg Berlin, 1973.
  • [8] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal of Mathematical Analysis and Applications, 58 (1), 135-146, 1977.
  • [9] L. Kuijken, H.V. Maldeghem and E.E. Kerre, Fuzzy projective geometries from fuzzy vector spaces, Information processing and management of uncertainty in knowledge-based systems. Editions Medicales et Scientifiques. Paris,La Sorbonne, 1331–1338, 1998.
  • [10] L. Kuijken, H.V. Maldeghem and E.E. Kerre, Fuzzy projective geometries from fuzzy groups, Tatra Mountains Mathematical Publications, 16, 85-108, 1999.
  • [11] L. Kuijken, Fuzzy projective geometries, Mathematics, Computer Science, EUSFLAT-ESTYLF Joint Conf., 1999.
  • [12] L. Kuijken and H.V. Maldeghem, Fibered geometries, Discrete Mathematics, 255, 259-274, 2002.
  • [13] L. Kuijken and H.V. Maldeghem, On the definition and some conjectures of fuzzy projective planes by Gupta and Ray, and a new definition of fuzzy building geometries, Fuzzy Sets and Systems, 138, 667-685, 2003.
  • [14] A. Rosenfeld, Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35, 512-517, 1971.
  • [15] L.A. Zadeh, Fuzzy sets, Information and Control, 8, 338-353, 1965.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Elif Altıntaş

Ayşe Bayar

Yayımlanma Tarihi 15 Nisan 2022
Gönderilme Tarihi 20 Mayıs 2021
Kabul Tarihi 20 Nisan 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 10 Sayı: 1

Kaynak Göster

APA Altıntaş, E., & Bayar, A. (2022). Fuzzy Collineations of Fuzzy Projective Planes. Konuralp Journal of Mathematics, 10(1), 166-170.
AMA Altıntaş E, Bayar A. Fuzzy Collineations of Fuzzy Projective Planes. Konuralp J. Math. Nisan 2022;10(1):166-170.
Chicago Altıntaş, Elif, ve Ayşe Bayar. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics 10, sy. 1 (Nisan 2022): 166-70.
EndNote Altıntaş E, Bayar A (01 Nisan 2022) Fuzzy Collineations of Fuzzy Projective Planes. Konuralp Journal of Mathematics 10 1 166–170.
IEEE E. Altıntaş ve A. Bayar, “Fuzzy Collineations of Fuzzy Projective Planes”, Konuralp J. Math., c. 10, sy. 1, ss. 166–170, 2022.
ISNAD Altıntaş, Elif - Bayar, Ayşe. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics 10/1 (Nisan 2022), 166-170.
JAMA Altıntaş E, Bayar A. Fuzzy Collineations of Fuzzy Projective Planes. Konuralp J. Math. 2022;10:166–170.
MLA Altıntaş, Elif ve Ayşe Bayar. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics, c. 10, sy. 1, 2022, ss. 166-70.
Vancouver Altıntaş E, Bayar A. Fuzzy Collineations of Fuzzy Projective Planes. Konuralp J. Math. 2022;10(1):166-70.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.