Fuzzy tangent line to a fuzzy circle (Q6606138)

Fuzzy geometry extends the notion of a fuzzy number to geometric objects like points, lines, line segments, angles etc. and investigates how and to which extend results of traditional Euclidean geometry can be transferred to this setting. This is not at all straightforward as equivalent properties of Euclidean geometry will often result in non-equivalent fuzzy concepts. Also uniqueness of fuzzy objects needs to be questioned anew.\N\NThe topic of this article is the definition of a fuzzy tangent line to a fuzzy circle. It proposes three different possible definitions, discusses conditions for their equivalence, and illustrates them in one example.\N\NThe first definition tries to capture the perpendicularity relation between circle radius and circle tangent and constructs the membership function by geometric transformations from fuzzy circle center and point of tangency. The second definition is more analytic than geometric and provides direct formulas for the tangent's membership function. The third definition is based on the (initially) real slope of the tangent and extends it to a fuzzy number.