Applying Soft Computing in Defining Spatial Relations [Hardcover]

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.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.- 2.1 Conceptual Neighborhoods.- 2.2 Fuzzification of Allen Relations.- 3 Applying Allens 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.- 2.1 Qualitative Distance Relations.- 2.2 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.- 1.1 Introduction.- 1.2 Modeling of Spatial Relations.- 1.3 Comparison of Definitions of Spatial Relations.- 1.4 Summary.- 2 Spatil33