Appendix II – Representations
Figure 23 shows the three representations considered in this report, the stacked bar chart, pie chart, and bubble chart.
Figure 23. Three possible representations of fuzzy traffic lights
These are just three of many ways to display "traffic lights" that have some resemblance to real traffic lights but have enough flexibility to be used to represent fuzzy lights, with more than one on at a time.
A simple representation which works for standard traffic lights but not for fuzzy ones is to use just one light and change the colour, either to red, yellow or green, or to a wider spectrum of colours as was suggested at the January workshop. By using just a single colour one loses the power of the fuzzy approach, which is to indicate the degree of discrepancy between indicators. The 2/3 approach suffers the same fault, and while it is probably easier to interpret a configuration that is part red and part yellow than one with just a single light that is a shade of orange, the amount of information in the two is the same (assuming that the shades of orange are continuous and distinguishable).
Of the three representations shown in Figure 23, the bubble diagram most resembles a traffic light, which has considerable merit. However, it suffers from two serious disadvantages. One is that it is a bit ambiguous, since it is not clear whether the area or the diameter of the lights is the quantity that represents the magnitude of the memberships. The second is that it is difficult to show the relative weighting of different indicators with a bubble diagram. For this reason one should be reluctant to use the bubble diagram representation unless it achieves a high level of user acceptance.
The other two forms avoid the first of these problems, since the size of the slices of pie or the height of the bar sections clearly represent the memberships. Both the diameter of the pie and the width of the bar can be used to indicate different weights, although with the circular pie chart it again is difficult to tell whether the area or the diameter of the pie is representative of the weight. This gives the exploded bar chart an advantage, as well as the fact that it more resembles a traffic light.