Abstract
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.
Keywords
Central Collineation Fuzzy Projective Plane Intuitionistic Fuzzy Projective Plane Projective Plane
References
- 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.
Abstract
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.
Keywords
Central Collineation Fuzzy Projective Plane Intuitionistic Fuzzy Projective Plane Projective Plane.
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | May 7, 2022 |
| Published in Issue | Year 2022 |