## Using Fuzzy Models in Spatial Simulation

In a geographic information system the data are stored in the form of raster data (uniformly spaced grid cells) or in the form of polygons. Grid data cells are more convenient for modeling approaches. An equally spaced grid cell is better suited to make simulation of fluxes with this data model. These simulations are, for example, important for wind or water erosion modeling. A fuzzy model needs continuous data as inputs. (An approximation with a discrete set with many members is also OK.) The spatial information is split into different information layers (maps) each containing a grid. A fuzz modeling approach usually needs two or three maps as inputs to calculate an output grid. The grids store information like soil quality, elevation data, land-use data, etc. Other data of this type are distances, such as between grid cells and points (nesting places for birds, location of wind energy plant, etc.) or between grid cells and linear features (roads, rivers, etc.). Another important example involving continuous data demonstrates the use of the so-called moving-window technique, which calculates qi =f x y) = // g(x-, y) dx dy [15]

Here A(x, y) is an area around the point (x, y) and g(x, y) is a function depending on spatial modeling problem. For simple problems, g(x, y) can be the mean or the median for all points in a region A(x, y). This technique produces a spatial abstraction of data at all grid cells. (Not only the value at the point, but also values in the neighborhood of the point are important.)

Before one can start using fuzzy models in spatial context, the spatial database must be provided. There are some steps that must be performed:

• select data sources for the project from the GIS database;

• transform the polygons to a grid using an appropriate resolution (the resolution depends on the modeling task; every process has its own scale);

• generate inputs for the fuzzy model using distances and the moving window technique.

This task has to be done in a GIS. To apply fuzzy models to this grid database, the modeler should prefer an integrated simulations system. Such a toolbox additionally provides a set of analysis tools. With these tools it is possible to analyze the spatial database, to explain the fuzzy model on concrete points, to control the rule base of the fuzzy model, etc. These tools should also be used to perform a validity test, which means that the model behavior should be checked against the expected correlations.