Analytical fuzzy plane geometry III

In this study, we attempt to construct fuzzy circles in a fuzzy geometrical plane. We provide a comprehensive study where we find a fuzzy number with a predetermined fuzzy distance from a given fuzzy number. We formulate fuzzy circles using the conventional basic definitions of crisp circles. Two different formulations of fuzzy circles are proposed, which depend on the information known about a fuzzy circle. The interrelations between the evaluated fuzzy circles are investigated. We show that the center of a fuzzy circle may not be a fuzzy point. However, the radius of a fuzzy circle that passes through three given fuzzy points is always a fuzzy number. The concepts of same and inverse points and a fuzzy number along a line are used to define and analyze the proposed ideas. Our discussions and studies are supported by suitable numerical and pictorial examples.