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Central Collineations in Fuzzy and Intuitionistic Fuzzy Projective Planes

Yıl 2022, Sayı: 35, 355 - 363, 07.05.2022
https://doi.org/10.31590/ejosat.1075566

Öz

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

Kaynakça

  • K.S. Abdukhalikov, The Dual of a Fuzzy Subspace, FSS 82 (1996) 375-381.
  • Z. Akc¸a, A. Bayar, S. Ekmekc¸i, H.V. Maldeghem, Fuzzy projective spreads of fuzzy projective spaces, Fuzzy Sets and Systems, 157(24) (2006) 3237–3247.
  • E. Altıntas¸ Kahriman, On Maps in Fuzzy and Intuitionistic Fuzzy Projective Planes, Eskis¸ehir Osmangazi University, Institute of Science, Doctoral Thesis, 2020.
  • K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
  • R. Baer, Projectivities with fixed points on every line of the plane. Bull. Amer. Math. Soc. 52 (1946) 273-286 .
  • E. A. Ghassan, Intuitionistic fuzzy projective geometry, J. of Al-Ambar University for Pure Science, 3 (2009) 1-5.
  • D. R. Hughes and F. C. Piper, Projective Planes, Springer-Verlag, New York Heidelberg, Berlin, 1973.
  • A. K. Katsaras, D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl. 58 (1) (1977) 135-146.
  • L. Kuijken, H.V. Maldeghem, 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, (1998) 1331–8.
  • L. Kuijken, H.V. Maldeghem, E.E. Kerre, Fuzzy projective geometries from fuzzy groups, Tatra Mt. Math. Publ. 16 (1999) 85-108.
  • L. Kuijken, Fuzzy projective geometries, Mathematics, Computer Science, EUSFLAT- ESTYLF Joint Conf., 1999.

Central Collineations in Fuzzy and Intuitionistic Fuzzy Projective Planes

Yıl 2022, Sayı: 35, 355 - 363, 07.05.2022
https://doi.org/10.31590/ejosat.1075566

Öz

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

Kaynakça

  • K.S. Abdukhalikov, The Dual of a Fuzzy Subspace, FSS 82 (1996) 375-381.
  • Z. Akc¸a, A. Bayar, S. Ekmekc¸i, H.V. Maldeghem, Fuzzy projective spreads of fuzzy projective spaces, Fuzzy Sets and Systems, 157(24) (2006) 3237–3247.
  • E. Altıntas¸ Kahriman, On Maps in Fuzzy and Intuitionistic Fuzzy Projective Planes, Eskis¸ehir Osmangazi University, Institute of Science, Doctoral Thesis, 2020.
  • K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
  • R. Baer, Projectivities with fixed points on every line of the plane. Bull. Amer. Math. Soc. 52 (1946) 273-286 .
  • E. A. Ghassan, Intuitionistic fuzzy projective geometry, J. of Al-Ambar University for Pure Science, 3 (2009) 1-5.
  • D. R. Hughes and F. C. Piper, Projective Planes, Springer-Verlag, New York Heidelberg, Berlin, 1973.
  • A. K. Katsaras, D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl. 58 (1) (1977) 135-146.
  • L. Kuijken, H.V. Maldeghem, 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, (1998) 1331–8.
  • L. Kuijken, H.V. Maldeghem, E.E. Kerre, Fuzzy projective geometries from fuzzy groups, Tatra Mt. Math. Publ. 16 (1999) 85-108.
  • L. Kuijken, Fuzzy projective geometries, Mathematics, Computer Science, EUSFLAT- ESTYLF Joint Conf., 1999.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Elif Altıntaş 0000-0002-3454-0326

Ayşe Bayar 0000-0002-2210-5423

Yayımlanma Tarihi 7 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 35

Kaynak Göster

APA Altıntaş, E., & Bayar, A. (2022). Central Collineations in Fuzzy and Intuitionistic Fuzzy Projective Planes. Avrupa Bilim Ve Teknoloji Dergisi(35), 355-363. https://doi.org/10.31590/ejosat.1075566