To improve the current GIS functions in describing geographic objects with fuzziness,this paper begins with a discussion on the distance measure of spatial objects based on the theory of sets and an introduction of dilation and erosion operators.Under the assumption that changes of attributes in a geographic region are gradual,the analytic expressions for the fuzzy objects of points,lines and areas,and the description of their formal structures are presented.The analytic model of geographic objects by means of fuzzy fields is developed.We have shown that the 9-intersection model proposed by Egenhofer and Franzosa (1991) is a special case of the model presented in the paper.
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