Geometric properties and relations play central roles in the description and processing of spatial data. The properties and relations studied by mathematicians usually have precise definitions, but verbal descriptions often involve imprecisely defined concepts such as elongatedness or proximity. The methods used in soft computing provide a framework for formulating and manipulating such concepts. This volume contains eight papers on the soft definition and manipulation of spatial relations and gives a comprehensive summary on the subject.

Fuzzifying Spatial Relations.- 1 Motivation.- 2 Imprecision in Spatial Relations.- 3 Applying Allen's Algorithm to Fuzzy Relations.- 4 Other Fuzzy Relations.- 5 Fuzzy Constraint Satisfaction.- 6 Conclusion.- Acknowledgement.- References.- Path Composition of Positional Relations Integrating Qualitative and Fuzzy Knowledge.- 1 Introduction.- 2 Composition of Positional Relations.- 3 Path Composition.- 4 Integrating Qualitative and Fuzzy Knowledge.- 5 Fuzzy Knowledge Coming from Particular Distance Systems.- 6 Conclusions.- Acknowledgments.- References.- Spatial Relations Based on Dominance of Fuzzy Sets.- 1 Spatial Relations.- 2 Spatial Relations Among Fuzzy Subsets.- References.- Mathematical Morphology and Spatial Relationships: Quantitative, Semi-Quantitative and Symbolic Settings.- 1 Introduction.- 2 Basic Morphological Operations, Fuzzy and Logical Extensions.- 3 Computing Spatial Relationships from Mathematical Morphology: Quantitative and Semi-Quantitative Setting.- 4 Spatial Representations of Spatial Relationships.- 5 Symbolic Representations of Spatial Relationships.- 6 Conclusion.- References.- Understanding the Spatial Organization of Image Regions by Means of Force Histograms: A Guided Tour.- 1 Introduction.- 2 The Notion of the Histogram of Forces.- 3 Comparing Force Histograms.- 4 Defining Fuzzy Spatial Relations.- 5 Generating Linguistic Spatial Descriptions.- 6 Conclusion.- Acknowledgments.- References.- Fuzzy Spatial Relationships and Mobile Agent Technology in Geospatial Information Systems.- 1 Introduction.- 2 Background.- 3 Fuzzy Directional Relationships and Querying.- 4 Extensions to the Model.- 5 Intelligent Agent Technology.- 6 Summary and Future Work.- Acknowledgments.- References.- Using Fuzzy Spatial Relations to Control Movement Behavior ofMobile Objects in Spatially Explicit Ecological Models.- 1 Introduction.- 2 Modeling Habitat Landscape.- 3 Fuzzy Control of Spatial Movement.- 4 Discussion.- References.- A Fuzzy Set Model of Approximate Linguistic Terms in Descriptions of Binary Topological Relations Between Simple Regions.- 1 Introduction.- 2 Related Literature.- 3 Fuzziness of Approximate Linguistic Terms - Preliminary Cognitive Evidences.- 4 A Fuzzy Set Model of Approximate Linguistic Terms.- 5 Discussion.- 6 Concluding Remarks.- Acknowledgements.- References.- About the Editors.