Visualizing fuzzy sets using opacity-varying freeform diagrams

Abstract

As an extension of classical sets, fuzzy sets allow their containing elements to have continuous membership, which broadens its applications in various domains. In order to visualize the uncertain owner–member relationship, we design an intuitive diagram to visualize fuzzy sets. The diagram has a freeform boundary, which allows a clear layout of the data. In addition, the opacity of the diagram reveals the uncertainty of the membership. Physical simulation and bi-harmonic interpolation are introduced to generate the proposed diagram. We test our method with different fuzzy sets. The results show that our method is efficient to generate intuitive visualization of fuzzy sets.

Visualizing Uncertainty in Sets

“…Prior work on visualizing defined uncertainty and set membership in (a) Venn diagrams [41] and (b) node-link diagrams [39] as well as visualizing uncertainty and set size in (c) treemaps [36] and (d) with circle packing [14].…”

“…In comparison to general uncertainty visualization, the representation of uncertain set data has received less attention. A few attempts exist (see Figure 2) for the visualization of fuzzy sets [39], [41], where set membership has a defined uncertainty. For set attributes, we are aware of only two prior works, which represent set size with a defined uncertainty in set hierarchies using a treemap [36] and a circle packing visualization [14].…”

Exhibiting Uncertainty: Visualizing Data Quality Indicators for Cultural Collections

“…Options for visualization: The visualization of uncertainty in sets did not receive much attention up to now [38]. For the visualization of fuzzy sets it has been suggested to position data points on rings with a different diameter within a circular set area, based on their probability [39], or to vary the opacity of the set area accordingly [40,41]. Aside from the position within a set area, the uncertainty of set membership of individual objects could also be encoded with varying transparency, or any other gradual modification of a glyph-as illustrated with selected techniques listed in Figure 4 (top row).…”