Qualified topological relations between spatial objects with possible vague shape

Broad boundary is generally used to replace one‐dimensional boundary for spatial objects with vague shape. For regions with broad boundary, this concept should respect both connectedness and closeness conditions. Therefore, some real configurations, like regions with partially broad boundary (e.g. lake with rocky and swamp banks), are considered invalid. This paper aims to represent different levels of shape vagueness and consider them during the identification of topological relations. Then, an object with vague shape is composed by two crisp components: a minimal extent and a maximal extent. Topological relations are identified by applying the 9‐Intersection model for the subrelations between the minimal and maximal extents of objects involved. Four subrelations are then represented through a 4‐Intersection matrix used to classify the topological relations. For regions with broad boundary, 242 relations are distinguished and classified into 40 clusters. This approach supports an adverbial expression of integrity constraints and spatial queries.

[1]  A. Schmitz,et al.  Modeling and manipulating fuzzy regions: strategies to define the topological relation between two fuzzy regions , 2006 .

[2]  F. Pinet,et al.  Fuzzy spatial objects and their topological relations , 2007 .

[3]  Nicholas Chrisman,et al.  THE ERROR COMPONENT IN SPATIAL DATA , 2005 .

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

[5]  Bin Li,et al.  Fuzzy Description of Topological Relations I: A Unified Fuzzy 9-Intersection Model , 2005, ICNC.

[6]  A. K. Bregt,et al.  Spatial Data Quality , 2008, Encyclopedia of GIS.

[7]  Peter A. Burrough,et al.  Fuzzy mathematical methods for soil survey and land evaluation , 1989 .

[8]  Christian S. Jensen,et al.  Indeterminacy and Spatiotemporal Data , 2003 .

[9]  François Pinet,et al.  A General Framework to Implement Topological Relations on Composite Regions , 2007, DEXA.

[10]  Yvan Bédard,et al.  Spatial Online Analytical Processing (SOLAP): Concepts, Architectures, and Solutions from a Geomatics Engineering Perspective , 2007 .

[11]  David Altman,et al.  Fuzzy Set Theoretic Approaches for Handling Imprecision in Spatial Analysis , 1994, Int. J. Geogr. Inf. Sci..

[12]  MAX J. EGENHOFER,et al.  Point Set Topological Relations , 1991, Int. J. Geogr. Inf. Sci..

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

[14]  Guy De Tré,et al.  The Applicability of Generalized Constraints in Spatio-Temporal Database Modelling and Querying , 2004 .

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

[16]  M. Smithson.  Ignorance and Uncertainty , 1989, Cognitive Science.

[17]  Arta Dilo,et al.  Representation of and reasoning with vagueness in spatial information : a system for handling vague objects , 2006 .

[18]  Jan Terje Bjørke,et al.  Topological relations between fuzzy regions: derivation of verbal terms , 2004, Fuzzy Sets Syst..

[19]  João L. G. Matos,et al.  Topological Relations using Two Models of Uncertainty for Lines , 2006 .

[20]  Zdzislaw Pawlak,et al.  Rough Sets Present State and Further Prospects , 1996, Intell. Autom. Soft Comput..

[21]  Daniel G. Brown,et al.  Classification and Boundary Vagueness in Mapping Presettlement Forest Types , 1998, Int. J. Geogr. Inf. Sci..

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

[23]  Adnan Yazici,et al.  Semantic data modeling of spatiotemporal database applications , 2001, Int. J. Intell. Syst..

[24]  François Pinet,et al.  Using UML and OCL to maintain the consistency of spatial data in environmental information systems , 2007, Environ. Model. Softw..

[25]  Robert Jeansoulin,et al.  Towards spatial data quality information analysis tools for experts assessing the fitness for use of spatial data , 2007, Int. J. Geogr. Inf. Sci..

[26]  Markus Schneider,et al.  A Design of Topological Predicates for Complex Crisp and Fuzzy Regions , 2001, ER.

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

[28]  Sanjiang Li,et al.  A fuzzy sets theoretic approach to approximate spatial reasoning , 2004, IEEE Transactions on Fuzzy Systems.

[29]  Guy De Tré,et al.  FUZZY REGIONS: THEORY AND APPLICATIONS , 2007 .

[30]  Nectaria Tryfona,et al.  Indeterminacy and Spatiotemporal Data: Basic Definitions and Case Study , 2005, GeoInformatica.

[31]  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.

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

[33]  Ola Ahlqvist,et al.  Using Rough Classification to Represent Uncertainty in Spatial Data , 1998 .

[34]  F. Benjamin Zhan,et al.  Topological relations between fuzzy regions , 1997, SAC '97.

[35]  Eliseo Clementini,et al.  A model for uncertain lines , 2005, J. Vis. Lang. Comput..

[36]  Max J. Egenhofer,et al.  Topological Error Correcting in GIS , 1997, SSD.

[37]  F. B. Zhan,et al.  Overlay of Two Simple Polygons with Indeterminate Boundaries , 2003, Trans. GIS.

[38]  Michael F. Goodchild,et al.  CHAPTER FOUR – Attribute accuracy , 1995 .

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

[40]  M. Andrea Rodríguez,et al.  Inconsistency Issues in Spatial Databases , 2005, Inconsistency Tolerance.

[41]  P.A.J. van Oort,et al.  Spatial data quality: from description to application , 2006 .

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

[43]  Markus Schneider,et al.  Vague Regions , 1997, SSD.

[44]  Y. Bédard.  UNCERTAINTIES IN LAND INFORMATION SYSTEMS DATABASES , 2008 .

[45]  Xinming Tang.  Spatial object model[l]ing in fuzzy topological spaces : with applications to land cover change , 2004 .

[46]  Andrew U. Frank,et al.  Tiers of ontology and consistency constraints in geographical information systems , 2001, Int. J. Geogr. Inf. Sci..

[47]  A. Cohn,et al.  A Taxonomy for Spatial Vagueness An Alternative Egg-Yolk Interpretation , 2001 .

[48]  Sungsoon Hwang,et al.  Modeling Localities with Fuzzy Sets and GIS , 2005 .

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

[50]  Stefano Spaccapietra,et al.  Uncertainty of Geographic Information and its Support in MADS , 2003 .

[51]  Michael F. Goodchild,et al.  Spatial Data Quality , 2002 .

[52]  Eliseo Clementini,et al.  Approximate topological relations , 1997, Int. J. Approx. Reason..

[53]  Hui Lin,et al.  Formalizing fuzzy objects from uncertain classification results , 2001, Int. J. Geogr. Inf. Sci..

[54]  Max J. Egenhofer,et al.  A Formal Definition of Binary Topological Relationships , 1989, FODO.

[55]  Models of uncertainty in spatial data , 2022 .

[56]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning with the Region Connection Calculus , 1997, GeoInformatica.

[57]  Anthony G. Cohn,et al.  Modelling Topological and Metrical Properties in Physical Processes , 1989, KR.

[58]  Gloria Bordogna,et al.  A Fuzzy Object-Based Data Model for Imperfect Spatial Information Integrating Exact Objects and Fields , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..