Fuzzy Collineations of Fuzzy Projective Planes
Year 2022,
Volume: 10 Issue: 1, 166 - 170, 15.04.2022
Elif Altıntaş
,
Ayşe Bayar
Abstract
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.
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Year 2022,
Volume: 10 Issue: 1, 166 - 170, 15.04.2022
Elif Altıntaş
,
Ayşe Bayar
References
- [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.
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- [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.