Fuzzy Reasoning about Geographic Regions
Reasoning about geographic regions, like forests, lakes, cities, etc., often involves uncertainty and imprecision. For example, when we talk about a region like the city of Auckland, we usually do not know exactly the boundaries of that region. Nevertheless, we are able to reason about such a region. Or if we hear on the radio that a cold front is moving in from Antarctica, we can estimate when it will reach New Zealand, although we might not be able to determine with certainty the exact relation between the area covered by the cold front and the one that is referred to as New Zealand.
Recently, the RCC theory has gained a particular interest in the AI research community as formalism to reason about regions. This first-order theory is based on a primitive relation, called connectedness, and uses eight topological relations, defined on the basis of connectedness, to provide a framework to reason about regions. Lehmann and Cohn have introduced an extension to the RCC theory, which deals with imprecision in spatial representations. Our work carries on from there by applying fuzzy sets to the RCC theory and introducing a uniform framework to reason about geographic regions under uncertainty and imprecision.
KeywordsSpatial Relation Cold Front Fuzzy Relation Membership Grade Fuzzy Reasoning
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- Bloch, I (2000) Spatial representation of spatial relationship knowledge. In Proc. KR-00, pp. 247–258, Breckenridge, Colorado.Google Scholar
- Cohn, A, Bennett, B, Gooday, J, and Gotts, N (1997) Representing and reasoning with qualitative spatial relations about regions. In Stock, O, editor, Spatial and Temporal Reasoning, pp. 97–134. Kluwer, Dordrecht, The Netherlands.Google Scholar
- Cohn, A and Gotts, N (1996) The ‘Egg-Yolk’ representation of regionswith indeterminate boundaries. In Burrough, P and Frank, A, editors, Geographical Objects with Undetermined Boundaries, GISDATA Series No. 2, pp. 171–187. Taylor and Francis, London, England.Google Scholar
- Cui, Z, Cohn, A, and Randell, D (1992) Qualitative simulation based on a logical formalism of space and time. In Proc. AAAI-92, pp. 679–684, San Jose, California.Google Scholar
- Freksa, C (1990) Qualitative spatial reasoning. In Proc. Workshop RAUM, pp. 21–36, Koblenz, Germany.Google Scholar
- Freuder, E and Wallace, R (1992) Partial constraint satisfaction. Artificial Intelligence, 58:21–70.Google Scholar
- Guesgen, H (1989) Spatial reasoning based on Allen’s temporal logic. Technical Report TR-89-049, ICSI, Berkeley, California.Google Scholar
- Guesgen, H (2002) From the egg-yolk to the scrambled-egg theory. In Proc. FLAIRS-02, pp. 476–480, Pensacola, Florida.Google Scholar
- Guesgen, H (2003) When regions start to move. In Proc. FLAIRS-03, pp. 465–469, St. Augustine, Florida.Google Scholar
- Guesgen, H, Hertzberg, J, and Philpott, A (1994) Towards implementing fuzzy Allen relations. In Proc. ECAI-94 Workshop on Spatial and Temporal Reasoning, pp. 49–55, Amsterdam, The Netherlands.Google Scholar
- Guesgen, H and Philpott, A (1995) Heuristics for solving fuzzy constraint satisfaction problems. In Proc. ANNES-95, pp. 132–135, Dunedin, New Zealand.Google Scholar
- Hernández, D (1991) Relative representation of spatial knowledge: The 2-D case. In Mark, D and Frank, A, editors, Cognitive and Linguistic Aspects of Geographic Space, pp. 373–385. Kluwer, Dordrecht, The Netherlands.Google Scholar
- Kettani, D and Moulin, B (1999) A spatial model based on the notions of spatial conceptual map and of object’s influence areas. In Freksa, C and Mark, D, editors, Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science, Lecture Notes in Computer Science 1661, pp. 401–416. Springer, Berlin, Germany.Google Scholar
- Lehmann, F and Cohn, A (1994) The EGG/YOLK reliability hierarchy: Semantic data integration using sorts with prototypes. In Proc. 3rd International Conference on Information and Knowledge Management (CIKM-94), pp. 272–279, Gaithersburg, Maryland.Google Scholar
- Mukerjee, A and Joe, G (1990) A qualitative model for space. In Proc. AAAI-90, pp. 721–727, Boston, Massachusetts.Google Scholar
- Musto, A, Stein, K, Eisenkolb, A, Röfer, T, Brauer, W, and Schill, K (2000) From motion observation to qualitative motion representation. In Freksa, C, Brauer, W, Habel, C, and Wender, K, editors, Spatial Cognition II: Integrating Abstract Theories, Empirical Studies, Formal Methods, and Practical Applications, Lecture Notes in Computer Science 1849, pp. 115–126. Springer, Berlin, Germany.Google Scholar
- Randell, D, Cui, Z, and Cohn, A (1992) A spatial logic based on regions and connection. In Proc. KR-92, pp. 165–176, Cambridge, Massachusetts.Google Scholar
- Renz, J (2001) A spatial odyssey of the interval algebra: 1. directed intervals. In Proc. IJCAI-01, pp. 51–56, Seattle, Washington.Google Scholar