CONSTRUCTING THE ELLİPSE AND ITS APPLICATIONS IN ANALYTICAL FUZZY PLANE GEOMETRY

Year 2023, Volume: 5 Issue: 1, 20 - 38, 22.08.2023

Seçil Özekinci Cansel Aycan

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

Abstract

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.

Keywords

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

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