Stratified Rough Sets and Vagueness
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The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in model-oriented generalization, also called semantic generalization, is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be applied to give generalized descriptions of subsets of the original set. The notion of equivalence relation, or partition, has recently been significantly extended by the introduction of the notion of a granular partition. A granular partition provides what may be thought of as a hierarchical family of partial equivalence relations. In this paper we show how the mechanisms for making rough descriptions with respect to an equivalence relation can be extended to give rough descriptions with respect to a granular partition. In order to do this, we also show how some of the theory of granular partitions can be reformulated; this clarifies the connections between equivalence relations and granular partitions. With the help of this correspondence we then can show how the notion of hierarchical systems of partial equivalence classes relates to partitions of partial sets, i.e., partitions of sets in which not all members are known. This gives us new insight into the relationships between roughness and vagueness.
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- Bit03.Bittner, T.: Indeterminacy and rough approximation. In: Proceedings of FLAIRS 2003, AAAI Press, Menlo Park (2003)Google Scholar
- BS03b.Bittner, T., Smith, B.: Vague reference and approximating judgments. Spatial Cognition and Computation 3(2) (2003)Google Scholar
- Jon97.Jones, C.B.: Geographical Information Systems and Computer Cartography. Longman, Harlow (1997)Google Scholar
- M+95.Müller, J.C., et al.: Generalization - state of the art and issues. In: Müller, J.C., Lagrange, J.P., Weibel, R. (eds.) GIS and Generalisation: Methodology and Practice, pp. 3–17. Taylor and Francis, London (1995)Google Scholar
- MLW95.Müller, J.C., Lagrange, J.P., Weibel, R. (eds.): GIS and Generalisation: Methodology and Practice. Taylor and Francis, London (1995)Google Scholar
- MMO90.Mislove, M., Moss, L., Oles, F.: Partial sets. In: Cooper, R., Mukai, K., Perry, J. (eds.) Situation Theory and Its Applications I. CSLI Lecture Notes, vol. 22, pp. 117–131. Center for the Study of Language and Information, Stanford (1990)Google Scholar
- PM97.Papadias, D., Egenhofer M.: Algorithms for hierarchical spatial reasoning. Geoinformatica 1(3) (1997)Google Scholar
- RS95.Rigaux, P., Scholl, M.: Multi-scale partitions: Application to spatial and statistical databases. In: Egenhofer, M.J., Herring, J.R. (eds.) SSD 1995. LNCS, vol. 951, Springer, Heidelberg (1995)Google Scholar
- SW98.Stell, J.G., Worboys, M.F.: Stratified map spaces:A formal basis for multi-resolution spatial databases. In: Poiker, T.K., Chrisman, N. (eds.) SDH 1998 Proceedings 8th International Symposium on Spatial Data Handling, pp. 180–189. International Geographical Union (1998)Google Scholar
- Wor98a .
- Yao99 .Yao, Y.Y.: Stratified rough sets and granular computing. In: Dave, R.N., Sudkamp, T. (eds.) Proceedings of the 18th International Conference of the North American Fuzzy Information Processing Society, pp. 800–804. IEEE Press, Los Alamitos (1999)Google Scholar