Characterization of Intuitionistic Fuzzy Collineations in Intuitionistic Fuzzy Projective Planes

Year 2022, Volume: 5 Issue: 4, 273 - 279, 01.12.2022

Elif Altıntaş , Ayşe Bayar

https://doi.org/10.33401/fujma.1049786

https://izlik.org/JA47YP34MN

Abstract

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

Keywords

Collineation , Intuitionistic Fuzzy , Intuitionistic Fuzzy Projective Plane , Isomorphism , Projective Plane

References

• [1] L. A. Zadeh, Fuzzy sets, Inf.Control, 8 (1965), 338-353.
• [2] L. Kuijken, H.V. Maldeghem, E.E. Kerre, Fuzzy projective geometries from fuzzy vector spaces, Proceedings 7th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, (1998), 1331–1338.
• [3] L. Kuijken, H.V. Maldeghem, E.E. Kerre, Fuzzy projective geometries from fuzzy groups, Tatra Mt. Math. Publ., 16 (1999), 85-108.
• [4] L. Kuijken, 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. Syst., 138 (2003), 667-685.
• [5] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst, 20 (1986), 87-96.
• [6] E. A. Ghassan, Intuitionistic fuzzy projective geometry, JUAPS, 3 (2009), 1-5.
• [7] P. K. Sharma, Homomorphism of Intuitionistic Fuzzy Groups, Int. Math. Forum, 6(64) (2011), 3169 - 3178.
• [8] B. Pekala, Properties of Atanassov’s intuitionistic fuzzy relations and Atanassov’s operators, Inf. Sci., 213 (2012), 84-93.
• [9] R., Pradhan, M., Pal, Intuitionistic Fuzzy Linear Transformations, APAM, 1(1) (2012), 57-68.
• [10] A. Bayar, S. Ekmekci, On some classical theorems in intuitionistic fuzzy projective plane, Konuralp J. Math., 3(1) (2015), 12-15.
• [11] Z. Akca, A. Bayar, S. Ekmekci, On the Intuitionistic Fuzzy Projective Menelaus and Ceva’s conditions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1) (2020), 891-899.
• [12] G. Cuvalcioglu, S. Tarsuslu (Yılmaz), Isomorphism Theorems on Intuitionistic FuzzyAbstract Algebras, CMA, 12(1), (2021), 109-126.
• [13] E. Altıntas¸, A. Bayar, Central Collineations in Fuzzy and Intuitionistic Fuzzy Projective Planes, EJOSAT, 35 (2022), 355-363.
• [14] E. Altıntas¸, A. Bayar, Fuzzy Collineations of Fuzzy Projective Planes, Konuralp J. Math., 10(1) (2022), 166-170.
• [15] K.S. Abdukhalikov, Fuzzy Linear Maps, J. Math. Anal. Appl. 220 (1998), 1-12.