CONSTRUCTING THE ELLİPSE AND ITS APPLICATIONS IN ANALYTICAL FUZZY PLANE GEOMETRY

Yıl 2023, , 20 - 38, 22.08.2023

Seçil Özekinci , Cansel Aycan

https://doi.org/10.54286/ikjm.1200814

Öz

In this paper, we studied about a detailed analysis of fuzzy ellipse. In the previously studies, some methods for fuzzy parabola are discussed (Ghosh and Chakraborty,2019). To define the fuzzy ellipse, it is necessary to modify the method applied for the fuzzy parabola. First, need to get five same points with the same membership grade to create crisp ellipse and the union of crisp ellipses passing through these points will form the fuzzy ellipse. Although it is difficult to determine the points with this property, it is important for constructing the fuzzy ellipse equation. In this study, we determine the points that satisfy this condition and prove the properties required to obtain the fuzzy ellipse to be formed by using these points. We have drawn a graph of a fuzzy ellipse and depicted the geometric location of fuzzy points with different membership grades on graph. We have also shown some geometric application on examples. In the third part of this study, it has been shown that the determinants defined in the calculation of the coefficients of the fuzzy ellipse can be calculated using the maple program for different points and angles with the examples given, thus different fuzzy ellipses can be obtained.

Anahtar Kelimeler

Fuzzy ellipse, fuzzy points, membership function, same fuzzy points, α- cuts

Kaynakça

• Referans1 Buckley, J.J., Eslami, E.(1997) “Fuzzy plane geometry I: points and lines”, Fuzzy Sets Syst., vol 86, 179–187.
• Referans2 Buckley, J.J., Eslami, E.(1997), “Fuzzy plane geometry II: circles and polygons”, Fuzzy Sets Syst., vol 87, 79–85.
• Referans3 Ghosh, D. Chakraborty D. (2012) “Analytical fuzzy plane geometry I”, Fuzzy Sets Syst., vol 209, 66–83.
• Referans4 Ghosh, D. Chakraborty, D. (2013)” Analytical fuzzy plane geometry II”, Fuzzy Sets Syst., vol 243, 84-109.
• Referans5 Ghosh, D. Chakraborty, D.(2016) “ Analytical fuzzy plane geometry III”, Fuzzy Sets Syst., vol 283, 83-107.
• Referans6 Ghosh, D. Chakraborty, D. (2019) “An Introduction to Analytical Fuzzy Plane Geometry”, Springer International Publishing, Cham,145-171.
• Referans7 Özekinci, S., Aycan C. (2022) Constructing a fuzzy hyperbola and its applications in analytical fuzzy plane geometry, Hindawi Journal of Mathematics, vol 2022, 1-16.
• Referans8 Rosenfeld, A.(1990) “Fuzzy rectangles”, Pattern Recognition Lett, vol 11, no.2, 677-679.
• Referans9 Rosenfeld, A. (1998) “Fuzzy geometry: An updated overview”, Inf. Sci, vol110, no.3-4, 127–133.
• Referans10 Zadeh, L.A. (2009) Toward extended fuzzy logic—a first step, Fuzzy Sets Syst., vol 160 ,3175–3181.
• Referans11 Zadeh, L.A. (1965) Fuzzy Sets, Information and Control, vol 8,338-353.
• Referans12 H.J. Zimmermann. (2001) Fuzzy Set Theory–and Its Applications, 4th edn. Springer, New York.