Professor Peter Fisher, of the University of Leicester, presented an EEO-AGI(S) seminar, titled “Digital Elevation Models as Fuzzy Numbers”. It not only dealt with DEMs, but discussed the issue of vagueness in geography and how this should be expressed and valued in GIS analyses.
The presentation began by exploring vagueness as a philosophical question and presenting its origins in the sorites paradox. It continued with explaining fuzzy sets and fuzzy logic and concentrated on vagueness of landforms, by proving the complexity and fuzziness of the simple – at first sight – question of where is a mountain.
Prof. Fisher introduced us to geomorphometry and showed how resolution is a determining factor in deciding the morphometric class of a feature. He also explained the morphometry technique proposed by Jo Wood and implemented within his Landserf GIS. Any landform can be categorised into one of the following classes: Channelness, Passness, Peakness, Pitness, Planarity and Ridgness. Out of these peakness is the one more evident and was presented in detail, illustrated with examples of fuzzy viewsheds for Helvellyn in the English Lake District. Also Type-2 fuzzy sets for higher order vagueness were presented and an example application for Munro Mountains in Scotland was shown.
Another question posed by Prof. Fisher was how to create zones of visual influence around vague objects. By vague objects he did not mean a philosophical entity but something real, like a farm, where the exact location of the individual fields was note recorded. He showed that fuzzy buffers provided a solution.
At this point he introduced us to the concept of DEM as a fuzzy surface. The need for a DEM with multiple elevation values per location emerged especially in the use of LIDAR, where the information recorded can be referring to one of many surfaces rather than the ground. An example of height change in a sand area was shown. Measures of minimum, median and maximum elevation were made and presented separately to overcome issues in visualisation and the change in land height was calculated as a fuzzy number.
Prof. Fisher concluded that fuzzy sets in Geographical Information Systems can bring better results to the analysis procedure, showing different aspects of the subject of interest, making way for different interpretations and more interesting analytical results and that there is still lot of work to be done in this field of study by enthusiastic researchers. For the audience it was a pleasure to listen to a passionate researcher and we thank him for his inspiring presentation.
(MSc in GIS at University of Edinburgh)