Ambiguous sets are defined as collections of events with uncertain or imprecise boundaries, characterized by four membership degrees: true, false, true-ambiguous, and false-ambiguous. This study investigates the measurement of distance within ambiguous sets, emphasizing two major contributions. First, it explores methods for calculating distances, including Euclidean distance (ED), normalized Euclidean distance (NED), Manhattan distance (MD), and normalized Manhattan distance (NMD). By analyzing these techniques, the research provides a comprehensive framework for understanding how each method quantifies the separation between events in ambiguous sets. Second, the study delves into the properties of these distance measurement methods concerning ambiguous sets.