Identifying Vector Feature Textures Using Fuzzy Sets

This paper describes a method to approach area-patch problems in model generalization using fuzzy set theory. The area patch problem identifies problems in generalizing areas (polygons) with the same semantics (feature code) but varying geometry and spatial distribution. Area-patch generalization can be understood as a pattern recognition problem with a variety of viable solutions, constrained by the purposes of the generalized output. In this research constraints are defined by common USGS cartographic measures for feature generalization. The vagueness, which is inherent in area-patch problems, stems from special cases such as archipelagos. Archipelagos are collections of polygons, any one of which may not contribute significantly to the pattern of the database, but may become prominent when conceptualized as a group. The paper demonstrates how to access the vague concept of archipelagos in a GIS environment using fuzzy sets to improve area patch generalization. We develop our method generalizing swamps and marshes in an NHD High-Resolution subbasin dataset spanning the Florida-Georgia border. Fuzzy membership functions are assigned for area, inter-polygon distance and number of neighbors within a predefined distance as known contributors to texture. These attributes are combined in a fuzzy overlay to derive degrees of memberships of polygons to the concept of a prototypical archipelago. The final delineation of archipelagos is based on 'alpha cuts' thresholding. A sensitivity analysis evaluates the impact of alpha-cuts on the resulting pattern recognition. For validation we compare the change in geometric properties (area, area/perimeter ratios) of polygons and overall texture from the original scale to the target scale between our approach and a solution that does not take into account archipelagos. Preliminary findings indicate that a fuzzy set approach allows for the capture of archipelagos, which would otherwise not be included in a generalization solution.