Union and intersection of Level-2 fuzzy regions

In many applications spatial data are considered, yet this data quite often are prone to uncertainty and imprecision. For this purpose, fuzzy regions have been developed. Our initial model, a fuzzy set over a two dimensional domain, allowed for both fuzzy regions and fuzzy points to be modelled. The model still had some shortcomings: all points where treated independently, and it was not possible to group points together. In some situations this makes the model more imprecise and uncertain than it should have been. Furthermore, while the model allowed for the representations of both fuzzy regions and fuzzy locations, simply by changing the interpretation of the fuzzy set, this interpretation needed to be specified as meta information. The model was extended to a level-2 fuzzy region to overcome these limitations, but this has an impact on operations. In this contribution, intersection and union will be discussed.