Fuzzy Modeling of Geometric Textures for Identifying Archipelagos in Area-Patch Generalization
Anderson-Tarver, Chris, Leyk, Stefan, Buttenfield, Barbara P., Cartography and Geographic Information Science
Fuzzy Logic and Generalization
With the introduction of Fuzzy Set Theory by Zadeh (1965) and its revolutionary concept that, due to inherent vagueness in defining classes of objects, an entity can be assigned partial or multiple memberships to one or several classes, there has been much discussion in recent years about the prospects of fuzzy logic for various GIS applications (Fisher 1992; Ahlqvist et al. 2003; Deng and Wilson 2008). While the debate over the intrinsic vagueness of geographic objects and their boundaries continues to the present day, fuzzy logic has proven to be a useful conceptual tool for GIScience researchers who want to analyze uncertainties, understand the limits of their conceptual models, and offer alternative viewpoints for delineation of geographic objects with indeterminate boundaries (Burrough 1996).
To the authors' knowledge, one area of GIS that has offered no published examples of a fuzzy logic implementation to a geographic problem is generalization. Generalization modifies information complexity, typically for display at a smaller scale but also for changes in map purpose, intended audience, or technical constraints (Slocum et al 2009). In a purely visual context, generalization as a form of abstraction refers to the discrepancy of a display from photorealism. Generalization, is also a type of information processing, that is, data modeling, used to tease out the knowledge deemed important for a given purpose. One significant aspect in generalization is the selection of crucial characteristics to display geographic essences, which depend always on a purpose (Brassel and Weibel 1988). As illustrated in Figure 1 generalization is one of three interrelated components (generalization, symbolization and production) of map design resulting from the interplay of abstraction and constraints (Buttenfield and Mark 1991).
[FIGURE 1 OMITTED]
Merging or aggregating vector features has been and continues to be a difficult task for automated generalization systems (Muller et al. 1995, Bundy et al. 1995, Steiniger and Weibel 2007). In fact, several authors use polygon aggregation to illustrate hurdles which must be addressed to implement holistic automatic generalization (Bertin 1983; Beard 1991; Steiniger and Weibel 2007). In broad terms one reason why automated polygon aggregation is so elusive is that many aspects of human pattern recognition are poorly understood and it is therefore difficult to formalize algorithms whose goal is to mirror a cognitive process which most people have as a natural acuity. In Figure 2, for example, the eye readily follows a sequence of small polygons which are aligned linearly or curvilinearly, even when these are embedded in a cluster of other polygons.
Moreover, many geographic concepts themselves are vague as they relate to the conceptual constraints of map design, especially when compound elements are involved, as in the concept of a settlement as comprised of a scatter of residential buildings. Vague concepts can be seen in mapping canyons, wetlands, or cultural phenomena such as the Corn Belt wherein boundaries cannot be delineated deterministically. Another example of a type of vague concept can be seen in object complexes such as road networks or fragmented forest lands with varying internal characteristics such as local density, local concentration, or local connectivity, which are difficult to identify automatically. In this paper, it is argued that a fuzzy logic approach to certain polygon aggregation problems is appropriate and advantageous in order to reconcile ambiguous feature continuum". Bertin was examining how best to preserve the structural pattern of the lacustrine area of Dombes, France (Figure 2) and thus to explain and resolve spatial relations between data items for display at a smaller scale. As Bertin alludes, multiple appropriate solutions can be derived for effective map design, but the challenge is to formalize criteria carefully and implement them consistently, according to the intended purpose. …