Given a sequence of n thematic maps which characterize a continuous cartographic temporal phenomenon for n instants , so that , we wish to predict the evolution of the temporal phenomenon at instant .

The different techniques that have been used to study the evolution are based on the tracking of particular points or segments of the studied objects. Such techniques require that the studied objects do not change their form. This is not the case in the examples of this work. We shall use a different method.

In [2], the forecasting method uses geographical data in vector representation and its fundamentals are based on the study of the position and shape of the spatial entities in each map. This method achieves a forecasting by means of different comparisons between attributes of regions. The final shapes and positions of the regions are determined by the use of the mathematical morphology in vectorial domain. The regions are constrained to uniform morphological transformations. Thus, this method assumes a uniform variation of the regions for the forecasting and does not take into account relevant land area features such as

• valleys, rivers, slopes, roads, villages and
• even regions frequently destroyed by fire.

Therefore, this method does not represent the reality because the existence of regions with different kinds of evolution is obvious. And besides, there are problems with the representation of the geographic world in a discretized way because vectors assume a hard-edged boundary.

A classic method which uses mathematical morphology over the forest regions of progression (growth) or regression was studied. But such a method only considers the shape and surface of regions and leaves out important factors which also influence the forestry evolution .

The approach proposed is similar to the latter approach mentioned above because we make use of regression and progression zones of the forest to determine the favorable directions of evolution (appearance or disappearance). However, forecasting is performed by coupling fuzzy set theory and out-image data. The advantage is that forecasting will consider the zones more or less favorable to the evolution and so the results will be more accurate.

We assume that forecasting may be approached by considering the following facts:

• the temporal events studied are continuous.
  
• the geographical data are in raster representation.