Fuzzy points: algebra and application

摘要

A fuzzy point is a region representing the uncertain location of a normal Euclidean point. A fuzzy point in the plane is considered to be a closed disk (a circle and its interior). The algebra of fuzzy points (which includes fuzzy vectors and fuzzy angles) is presented. Since fuzzy points are represented as closed disks, the lengths of fuzzy vectors, and the angles between fuzzy vectors can be viewed as properties of circles in the plane. Methods to compute the magnitude of a fuzzy angle are given. An application of fuzzy point algebra to the problem of detecting and tracking storms in Doppler radar image sequences, which motivates this work, is discussed.