Nowadays Geographical Information Systems (GIS) and spatial database systems are mainly able to handle crisp spatial objects, i.e., objects in space whose locations, extents, shapes, and boundaries are precisely determined. However, geoscientists and advanced GIS applications are increasingly interested in handling spatial objects that are characterized by the feature of spatial fuzziness and do not have sharp but blurred boundaries and/or interiors; hence, we call them fuzzy spatial objects. Examples are air polluted areas and temperature zones. In the same way as fuzzy spatial objects are blurred, the topological relationships (e.g., overlap, inside) between them are blurred too. In this conceptual paper, we propose a novel model to formally define fuzzy topological relationships for simple and complex fuzzy regions. Such a fuzzy relationship computes a membership degree between 0 and 1 that indicates to which extent this relationship holds. It is mapped to a high-level fuzzy modifier and transformed into a Boolean predicate that can be embedded into spatial queries.

The use of a spatial index is a common strategy to improve the performance of spatial queries in spatial database systems and Geographic Information Systems. Choosing the right spatial index to be employed in a given context requires a quantitative method to analyze the performance of spatial indices. This is done through extensive experimental evaluations. However, conducting these evaluations is an expensive, error-prone, and challenging task because (i) spatial objects are complex data to manage, (ii) spatial indices can apply different parameter values and thus assume distinct configurations, and (iii) there are indices specifically developed for different storage systems, such as disks and flash memories. In this article, we propose FESTIval, a versatile framework for conducting experimental evaluations of spatial indices. FESTIval has the following main advantages: •the support for different types of disk-based and flash-aware spatial indices;•the specification and execution of user-defined workloads;•the use of a data schema that stores index configurations and statistical data of executed workloads. Because of its characteristics, FESTIval allows users to reproduce executed experiments. Further, FESTIval provides an extensible environment, where any spatial dataset can be handled by spatial indices. FESTIval has been used to validate new proposals of flash-aware spatial indices, such as eFIND-based indices.

Many geographical applications have to deal with spatial objects that reveal an intrinsically vague or fuzzy nature. A spatial object is fuzzy if locations exist that cannot be assigned completely to the object or to its complement. Spatial database systems and Geographical Information Systems are currently unable to cope with this kind of data. Based on an available abstract data model of fuzzy spatial data types for fuzzy points, fuzzy lines, and fuzzy regions, this paper proposes the Spatial Plateau Algebra that provides spatial plateau data types as an executable type system for fuzzy spatial data types. Each spatial plateau object consists of a finite number of crisp counterparts that are all adjacent or disjoint to each other, are associated with different membership values, and hence form different plateaus. The formal framework and the implementation are based on well known, exact models and available implementations of crisp spatial data types. Spatial plateau set and metric operations as well as spatial plateau topological predicates on spatial plateau objects are expressed as a combination of geometric methods on the underlying crisp spatial objects. This paper offers a conceptually clean specification for implementing a database extension for fuzzy spatial objects and their operations and predicates. Further, we demonstrate the embedding of these new data types as attribute data types in a database schema as well as the incorporation of fuzzy spatial operations and predicates into a database query language.