Fuzzy and Rough Set Approaches for Uncertainty in Spatial Data

1 Abstract. The management of uncertainty in databases is necessary for real world applications, especially for systems involving spatial data such as geographic in- formation systems. Rough and fuzzy sets are important techniques that can be used in various ways for modeling uncertainty in data and in spatial relationships between data entities. This chapter discusses various approaches involving rough and fuzzy sets for spatial database applications such as GIS.

[1]  W. Shi,et al.  ROUGH SPATIAL DESCRIPTION , 2002 .

[2]  Valerie V. Cross,et al.  Fuzzy objects for geographical information systems , 2000, Fuzzy Sets Syst..

[3]  Dimitris Papadias,et al.  Processing fuzzy spatial queries: a configuration similarity approach , 1999, Int. J. Geogr. Inf. Sci..

[4]  Shuliang Wang,et al.  Rough Spatial Interpretation , 2004, Rough Sets and Current Trends in Computing.

[5]  Michael F. Goodchild,et al.  Foundations of Geographic Information Science , 2003 .

[6]  Lars Kulik,et al.  A Graded Approach to Directions between Extended Objects , 2002, GIScience.

[7]  Roy Ladner,et al.  Fuzzy Set Approaches to Spatial Data Mining of Association Rules , 2003, Trans. GIS.

[8]  M. Egenhofer,et al.  Point-Set Topological Spatial Relations , 2001 .

[9]  John F. Roddick,et al.  Temporal, Spatial, and Spatio-Temporal Data Mining , 2001, Lecture Notes in Computer Science.

[10]  F. Petry,et al.  Modeling spatial relationships within a fuzzy framework , 1998 .

[11]  Theresa Beaubouef,et al.  EXTENSION OF THE RELATIONAL DATABASE AND ITS ALGEBRA WITH ROUGH SET TECHNIQUES , 1995, Comput. Intell..

[12]  Antonin Guttman,et al.  R-trees: a dynamic index structure for spatial searching , 1984, SIGMOD '84.

[13]  M. Goodchild,et al.  Uncertainty in geographical information , 2002 .

[14]  W. Shi,et al.  UNCERTAINTY-BASED SPATIAL DATA MINING , 2003 .

[15]  Chris Cornelis,et al.  Fuzzy region connection calculus: Representing vague topological information , 2008, Int. J. Approx. Reason..

[16]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[17]  Fangju Wang,et al.  A fuzzy grammar and possibility theory-based natural language user interface for spatial queries , 2000, Fuzzy Sets Syst..

[18]  F. Petry,et al.  Approximation of topological relations on fuzzy regions: an approach using minimal bounding rectangles , 2003, 22nd International Conference of the North American Fuzzy Information Processing Society, NAFIPS 2003.

[19]  Richard Bellman,et al.  On the Analytic Formalism of the Theory of Fuzzy Sets , 1973, Inf. Sci..

[20]  Xinming Tang,et al.  Fuzzy Topological Relations Between Fuzzy Spatial Objects , 2006, FSKD.

[21]  R. A. MacMillan,et al.  A generic procedure for automatically segmenting landforms into landform elements using DEMs, heuristic rules and fuzzy logic , 2000, Fuzzy Sets Syst..

[22]  John G. Stell,et al.  Spatial relations between indeterminate regions , 2001, Int. J. Approx. Reason..

[23]  Chris Cornelis,et al.  Fuzzy region connection calculus: An interpretation based on closeness , 2008, Int. J. Approx. Reason..

[24]  Theresa Beaubouef,et al.  Spatial data methods and vague regions: A rough set approach , 2007, Appl. Soft Comput..

[25]  M. Worboys.  Computation with imprecise geospatial data , 1998 .

[26]  M. Worboys,et al.  A formal approach to imperfection in geographic information , 2001 .

[27]  Martine De Cock,et al.  Spatial reasoning in a fuzzy region connection calculus , 2009, Artif. Intell..

[28]  G. De Tré,et al.  A generalised object-oriented database model with generalised constraints , 1999, NAFIPS 1999.

[29]  Michael F. Worboys,et al.  Imprecision in Finite Resolution Spatial Data , 1998, GeoInformatica.

[30]  M. Worboys,et al.  A FORMAL ONTOLOGICAL APPROACH TO IMPERFECTION IN GEOGRAPHIC INFORMATION Full paper , 2000 .

[31]  A. Morris,et al.  A Framework for Modeling Uncertainty in Spatial Databases , 2003, Trans. GIS.

[32]  Peter A. Burrough,et al.  Natural Objects with Indeterminate Boundaries , 2020 .

[33]  Ola Ahlqvist,et al.  Rough classification and accuracy assessment , 2000, Int. J. Geogr. Inf. Sci..

[34]  Frederick E. Petry,et al.  Fuzzy Modeling with Spatial Information for Geographic Problems , 2008 .

[35]  Stephen J. Ventura,et al.  Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin , 1997 .

[36]  Sadaaki Miyamoto,et al.  Rough Sets and Current Trends in Computing , 2012, Lecture Notes in Computer Science.

[37]  Stephan Winter,et al.  Spatial Information Theory, 8th International Conference, COSIT 2007, Melbourne, Australia, September 19-23, 2007, Proceedings , 2007, COSIT.

[38]  A. Skidmore.  Terrain position as mapped from a gridded digital elevation model , 1990 .

[39]  Tamás D. Gedeon,et al.  Spatial Interpolation Using Fuzzy Reasoning , 2003, Trans. GIS.

[40]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[41]  Hans W. Guesgen,et al.  Fuzzifying spatial relations , 2002 .

[42]  Markus Schneider,et al.  Spatial Data Types for Database Systems , 1997, Lecture Notes in Computer Science.

[43]  Thomas Bittner,et al.  Rough Sets in Spatio-temporal Data Mining , 2000, TSDM.

[44]  Suzana Dragicevic.  Multi-Dimensional Interpolations with Fuzzy Sets , 2005 .

[45]  Paul S. Fisher,et al.  Boolean and Fuzzy Regions , 1996 .

[46]  Zdzislaw Pawlak,et al.  On Conflicts , 1984, Int. J. Man Mach. Stud..

[47]  J. H. D. Keukelaar,et al.  Topics in Soft Computing , 2002 .

[48]  Michalis Vazirgiannis,et al.  Uncertainty handling in spatial relationships , 2000, SAC '00.

[49]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[50]  Soumitra Dutta,et al.  Approximate spatial reasoning: Integrating qualitative and quantitative constraints , 1991, Int. J. Approx. Reason..

[51]  Wenzhong Shi,et al.  A fuzzy topology for computing the interior, boundary, and exterior of spatial objects quantitatively in GIS , 2007, Comput. Geosci..

[52]  Frederick E. Petry,et al.  Fuzzy Minimum Bounding Rectangles , 2004 .

[53]  Thomas Bittner,et al.  Stratified Rough Sets and Vagueness , 2003, COSIT.

[54]  W. Pedrycz,et al.  An introduction to fuzzy sets : analysis and design , 1998 .

[55]  Theresa Beaubouef,et al.  Rough set spatial data modeling for data mining , 2004, Int. J. Intell. Syst..

[56]  A-Xing Zhu,et al.  Fuzzy Representation of Special Terrain Features Using a Similarity-based Approach , 2005 .

[57]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[58]  S. Gale.  Inexactness, Fuzzy Sets, and the Foundations of Behavioral Geography* , 2010 .

[59]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[60]  P. Burrough,et al.  Geographic Objects with Indeterminate Boundaries , 1996 .

[61]  F. Benjamin Zhan,et al.  Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries , 1998, Soft Comput..

[62]  Guy De Tré,et al.  Field Based Methods for the Modeling of Fuzzy Spatial Data , 2005 .

[63]  R. Yager.  On a general class of fuzzy connectives , 1980 .

[64]  Thomas Bittner,et al.  Approximate qualitative spatial reasoning , 2001, Spatial Cogn. Comput..

[65]  Suzana Dragicevic,et al.  A fuzzy set approach for modelling time in GIS , 2000, Int. J. Geogr. Inf. Sci..

[66]  J. Goguen.  L-fuzzy sets , 1967 .