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

Abstract

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.

Modeling fuzzy topological predicates for fuzzy regions

“…Additionally, their implementation and their mappings to Boolean topological predicates will be studied as well. Our goal is to perform the implementation in the context of the Spatial Plateau Algebra [4], which provides a general concept for the implementation of fuzzy spatial data types.…”

A Graph-Based Spatiotemporal Data Framework for 4D Natural Phenomena Representation and Quantification–An Example of Dust Events

“…Geo-dipoles represent the interactions based on the locations of geo-atoms, such as the direction, the distance, the interaction, and the flow. Since natural phenomena generally do not have crisp boundaries, they are broadly represented as fuzzy spatial objects in spatiotemporal databases [26,27], thus providing a flexible query and reasoning on imperfect spatial and temporal information [28]. Object-oriented database models were also developed to store, manage, query, and index fuzzy spatial objects with information imperfectness [29].…”

Qualitative topological relations between interval type‐2 fuzzy spatial objects

“…Models based on multiple‐valued logic use a set of discrete values to represent membership values of fuzzy geographical objects [e.g. the spatial plateau algebra (SPA) model; Schneider, ]. These models are finer than previous models, but not fine enough to express the uncertainty of fuzzy spatial objects and phenomena.…”

“…Over the past 20 years, many studies in the field of geographic information systems (GIS) and spatial database domains have focused on models of fuzzy geographical objects and their relationships, because the shapes of many spatial objects are inherently vague (e.g. residential centers, polluted rivers, forests) (Bloch, ; Dilo, ; Du et al, ; Guo, & Cui, ; Liu & Shi, ; Schneider, ; Schneider, ; Wang, Du, Feng, Zhang, & Zhang, ; Zhan, ). Molenaar () introduced three definition levels of fuzzy objects, and extensional uncertainty plays a dominant role in the spatial representation of fuzzy objects.…”