Constructing the Fuzzy Hyperbola and Its Applications in Analytical Fuzzy Plane Geometry

Abstract

In this paper, we studied about a detailed analysis of fuzzy hyperbola. In the previous studies, some methods for fuzzy parabola are discussed (Ghosh and Chakraborty, 2019). To define the fuzzy hyperbola, it is necessary to modify the method applied for the fuzzy parabola. To obtain a conic, it is necessary to know at least five points on this curve. First of all, in this study, we examined how to detect these five fuzzy points. We have discussed in detail the impact of points in this examination on finding fuzzy membership degrees and determining the curve. We show the use of the algorithm for calculating the coefficients in the conic equation on the examples. We make detailed drawings of all the fuzzy hyperbolas found and depicted the geometric location of fuzzy points with different membership degrees on the graph. As can be seen from the figures in our study, the importance of membership degrees in fuzzy space is that it causes us to find different numbers of hyperbola curves for the five points we study with. In addition, finding the membership of a given point to the fuzzy hyperbola is possible by solving nonlinear equations under different angular approaches. This examination is shown in detail in this study, and the results in the examples are evaluated by geometric comments. The systems formed by the fuzzy hyperbola curves are found to have different areas of use, as presented in the Conclusion. Some of usage areas of fuzzy hyperbola are radar systems, scanning devices, photosynthesis, heat, and CO2 distribution of plants.

Constructing the Elli̇pse and Its Applications in Analytical Fuzzy Plane Geometry

“…(𝑥 − 1) We find them and replace in (7) then we obtain the following non-linear equation which determinants But we get 0.85 from 0 to 1 from these real two values.…”

“…A fuzzy parabola that passes through five fuzzy points are constructed by Ghosh and Chakraborty in the study [6]. Then Özekinci and Aycan introduced a method to construct a fuzzy hyperbola and made applications about fuzzy hyperbola [7].…”

“…Now let write five same-points on 𝐸 ̅ 1 , 𝐸 ̅ 2 , 𝐸 ̅ 3 , 𝐸 ̅ 4 and 𝐸 ̅ 5 whose membership degrees are Then we put 𝜃 0 = 45° in(7) and we calculate 𝑎 𝜃 𝛼 , 𝑏 𝜃 𝛼 , 𝑔 𝜃 𝛼 , 𝑓 𝜃 𝛼 and 𝑐 𝜃 𝛼 .…”