Algorithms for Buffering Fuzzy Maps

In this paper, we show how standard GIS operations like the complement, union, intersection, and buffering of maps can be made more flexible by using fuzzy set theory. In particular, we present a variety of algorithms for operations on fuzzy maps, focusing on buffer operations for fuzzy maps. Introduction Although geographic information systems have been used for quite a while (Coppock & Rhind 1991), their functionality has changed only little over the years. In spite of their name, geographic information systems have so far been mostly geometric in nature, ignoring the temporal, thematic, and qualitative dimensions of geographic features (Molenaar 1996; Sinton 1978; Usery 1996). There are numerous attempts to overcome these limitations. For example, a variety of papers (Frank 1992; Goodchild 1992; Gupta, Weymouth, & Jain 1991; Herring 1991; 1992; Raper & Maguire 1992) deal with extensions of the data model, while Allen’s work and its derivatives (Allen 1983; Freksa 1990; Guesgen 1989; Hernández 1991; Mukerjee & Joe 1990) form the basis for numerous temporal and qualitative endeavors to extend geographic information systems (Egenhofer & Golledge 1997; Frank 1994; 1996; Peuquet 1994). Applications of fuzzy techniques are most commonly found in remote sensing literature but (Altmann 1994; Brimicombe 1997; Molenaar 1996; Plewe 1997) provide examples that the inherent fuzziness of geographic features becomes increasingly acknowledged in geographic information science as well. In many geographic information systems, the extraction of new information from stored spatial data is achieved through map overlap. New maps are computed from existing ones by applying one of the following operations: Buffer operations, which increases the size of an object by extending its boundary. Set operations, such as complement, union, and intersection. These operations are exact quantitative operations. Humans, on the other hand, often prefer a vague, uncertain, or qualitative operation over an exact quantitative one. For example, instead of requesting all locations on a map that Copyright c 2001, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. are at most 2810m away from the sea, it would be more adequate from the cognitive viewpoint to request all location that are close to the sea (Clementini, Di Felice, & Hernández 1997). This, however, requires some kind of vague, uncertain, or qualitative buffer operation. We have introduced such an operation, together with other similar operations, in previous papers (Guesgen & Albrecht 1998; Guesgen & Histed 1996) by using fuzzy set theory, but have not discussed efficient algorithms for the fuzzy operations.