C 
1 : flv )23.0 
-2.0 p 
fA*(v p) = Rs 2 20 : 2.0«fiv «3.0 (2) 
0 : flv 0:20 
where f(v,) = rainfall in centimeters of the pixel in a 
raster image of rainfall. 
Both of these examples have been developed on the basis of 
a raster geometric image in which the pixel values can be 
assigned real number values in the closed interval [0,1]. 
4. CONCLUSIONS 
The development of representational methods for fuzzy 
features offers the potential to improve the accuracy of 
analytical results from GIS analysis. While the examples 
presented are simplistic cases relying on spatial and 
thematic attributes of geographic datasets in raster formats, 
more complex fuzzy set functions can be formed in a 
similar manner by changing the fuzzy interpolation 
functions from linear to polynomial and other non-linear 
functions. The use of spatial position as the defining 
parameter of fuzziness allows the same function to be used 
in a variety of image representations of the same feature. 
Use of thematic values as the defining parameter necessarily 
limits the function to a single image type. The use of a 
comprehensive framework which supports multiple 
representations and multiple data sources appears to hold 
promise for applications requiring analysis of many datasets. 
While the current trend toward feature-based 
implementations (sometimes using object-oriented computer 
science approaches) of GIS holds promise for better user 
interfaces and the shielding of users from the complexities 
of geometric manipulation of geographic features, the 
strength of these approaches appear to be in allowing 
multiple representations within a GIS for a single 
geographical entity. Fuzzy sets offer one approach to 
representing geographic features with indeterminate 
boundaries with spatial, thematic, and in the future, 
temporal attributes and relationships defining the extent of 
the fuzzy set function. 
Future research should include development of specific 
applications to test the fuzzy set representations in the 
feature-based approach. Among such applications, 
representation of agricultural phenomena with fuzzy spatial 
extents and fuzzy functions defined by thematic parameters 
such as phosphorus, potassium, nitrogen, soil ph, and other 
attributes show promise. 
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