Crisp Spatial Objects Research Articles

Fsr: An R package for fuzzy spatial data handling

AbstractSpatial libraries are core components in many geographic information systems, spatial database systems, and spatial data science projects. These libraries provide the implementation of spatial type systems that include spatial data types and a large diversity of geometric operations. Their focus relies on handling crisp spatial objects, which are characterized by an exact location and a precisely defined extent, shape, and boundary in space. However, there is an increasing interest in analyzing spatial phenomena characterized by fuzzy spatial objects, which have inexact locations, vague boundaries, and/or blurred interiors. Unfortunately, available spatial libraries do not provide support for fuzzy spatial objects. In this article, we describe the R package named fsr, which is based on the Spatial Plateau Algebra and is publicly available at https://cran.r‐project.org/package=fsr. Our tool provides methods for building fuzzy spatial objects as spatial plateau objects and conducting exploratory spatial data analysis by using fuzzy spatial operations.

Spatial Plateau Algebra for implementing fuzzy spatial objects in databases and GIS: Spatial plateau data types and operations

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 (GIS) 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 that leverages fuzzy set theory and fuzzy point set topology, this article proposes a Spatial Plateau Algebra that provides spatial plateau data types as an implementation of 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 implementations of crisp spatial data types. Spatial plateau operations as geometric operations on spatial plateau objects are expressed as a combination of geometric operations on the underlying crisp spatial objects. This article offers a conceptually clean foundation for implementing a database extension for fuzzy spatial objects and their operations, and demonstrates the embedding of these new data types as attribute data types in a database schema as well as the incorporation of fuzzy spatial operations into a database query language.

Topological relations between fuzzy regions in a fuzzy topological space

Topological relations are one of the most important aspects in GIS modeling. The topological relations between crisp spatial objects have been well identified. However, the topological relations between fuzzy spatial objects need more investigation. This paper deals with building a special fuzzy topological space for fuzzy sets. Based on it, a formal definition of simple fuzzy region is given. A 4×4-intersection and furthermore a 5×5-intersection approach are proposed for the formalism of topological relations. Finally 152 topological relations between two simple fuzzy regions are identified based on the 4×4-intersection approach in R2.

OCL for formal modelling of topological constraints involving regions with broad boundaries

Integrity constraints can control topological relations of objects in spatial databases. These constraints can be modelled using formal languages such as the spatial extension of the Object Constraint Language (Spatial OCL). This language allows the expression of topological integrity constraints involving crisp spatial objects but it does not support constraints involving spatial objects with vague shapes (e.g. forest stand, pollution zone, valley or lake). In this paper, we propose an extension of Spatial OCL based on (1) a geometric model for objects with vague shapes, and (2) an adverbial approach for modelling topological constraints involving regions with broad boundaries. This new language provides an easiness in the formal modelling of these complex constraints. Our approach has been implemented in a code generator. A case study is also presented in the paper in the field of agriculture spreading activities. AOCL OVS takes account of the shape vagueness of spread parcel and improve spatial reasoning about them.