Fuzzy Collineations of Fuzzy Projective Planes

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,

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[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.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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