Interactive Visualization of Fuzzy Set Operations

Fuzzy sets refer to the datasets which do not have separate, distinct clusters, and they contain data elements whose membership values are between 0 and 1. Often each element belongs to several groups. We design a disk diagram with an augmented frequency graph to visualize elements in a fuzzy set. It shows the distribution of the elements within the set with respect to the membership function value. Fuzzy set operations-like intersection-are used to find the elements of interests with certain degree of confidence. However, few techniques exist for visualization of fuzzy set operations whose process and result provide both the relationship and the distribution of individual data point between sets. With the proposed disk diagram representing a fuzzy set, we suggest an interactive visualization system to analyze fuzzy data and grasp the relationship among the sets. By interactively overlapping the disk diagrams, a user can not only bring out the individual elements of interests, but also overview the whole data elements associated with the sets. Furthermore, we investigated two different visualization scenarios for intuitive interpretation of the visualization results. We demonstrate the proposed visualization system with a terrorist analysis output dataset.