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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.

Keywords

Collineation Fuzzy Projective Plane Isomorphism Projective Plane

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.
  • [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.

Year 2022, Volume: 10 Issue: 1, 166 - 170, 15.04.2022

Elif Altıntaş Ayşe Bayar

Abstract

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.
  • [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.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elif Altıntaş

Ayşe Bayar

Publication Date April 15, 2022
Submission Date May 20, 2021
Acceptance Date April 20, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

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. April 2022;10(1):166-170.
Chicago Altıntaş, Elif, and Ayşe Bayar. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 166-70.
EndNote Altıntaş E, Bayar A (April 1, 2022) Fuzzy Collineations of Fuzzy Projective Planes. Konuralp Journal of Mathematics 10 1 166–170.
IEEE E. Altıntaş and A. Bayar, “Fuzzy Collineations of Fuzzy Projective Planes”, Konuralp J. Math., vol. 10, no. 1, pp. 166–170, 2022.
ISNAD Altıntaş, Elif - Bayar, Ayşe. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics 10/1 (April 2022), 166-170.
JAMA Altıntaş E, Bayar A. Fuzzy Collineations of Fuzzy Projective Planes. Konuralp J. Math. 2022;10:166–170.
MLA Altıntaş, Elif and Ayşe Bayar. “Fuzzy Collineations of Fuzzy Projective Planes”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 166-70.
Vancouver Altıntaş E, Bayar A. Fuzzy Collineations of Fuzzy Projective Planes. Konuralp J. Math. 2022;10(1):166-70.
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