Conics in analytical fuzzy plane geometry and their applications

The aim of this thesis is to create Fuzzy parabola, Fuzzy ellipse, and Fuzzy hyperbola. Fuzzy conics that passing through the five same fuzzy points are obtained by using the most applicable method among the discussed methods to create a fuzzy parabola. In the first section, the short history of this subject is presented. Firstly, information is given about the reason for the emergence of Fuzzy logic and its usage areas. Studies in geometry related to Fuzzy logic and the general properties of this studies have been mentioned. Then, the preliminary information about the study and the definitions that will be used in the next chapters are given. In the second section, some methods for obtaining a Fuzzy parabola in the fuzzy space are discussed and the most accurate method to obtain this parabola has been determined, its geometric properties have been examined. Then various geometric applications have given. In the third section, necessary studies have been done to obtain a Fuzzy ellipse. Suitable changes are made in the method which used to obtain a Fuzzy parabola in the previous section and a Fuzzy ellipse has been created. Five same points have been taken on the core ellipse and a Fuzzy ellipse which passing through the points has been created. Then, the membership value of a point in this Fuzzy ellipse has been calculated and the applications have been given to form the equation of the Fuzzy ellipse that cover this point and the graph of the fuzzy ellipse is drawn. In addition, a new algorithm has been created to generate Fuzzy ellipses. In the fourth section, the necessary theorems have been obtained by making changes for the Fuzzy hyperbola in the method used in the second and third sections, and the Fuzzy hyperbola has been created. The steps applied in obtaining the fuzzy hyperbola have been depicted on the graph and geometric comments have been obtained by making applications a Fuzzy hyperbola. In these examples, the value of membership of any point to the Fuzzy hyperbola has been investigated and the fuzzy hyperbola equation which passing through these points have been obtained and a new algorithm has been created to obtain fuzzy hyperbola. So, calculations have been made in a short time and the Fuzzy hyperbola has been drawn. In the fifth section, the result can be derived from the thesis are included.