Using Tin-Based Structures for the Modelling of Fuzzy Gis Objects in a Database

Abstract

Traditional databases can manage only crisp information, a limitation that also holds for geographic information systems and spatial databases. In this paper, we present a technique based on triangulated irregular networks (or TINs for short) and fuzzy set theory to model imprecise or uncertain regions. A fuzzy region is represented by a Extended TIN, which allows for an associated value for each point of the region in the presented approach to be considered; this associated value will be a membership grade. As is common in fuzzy set theory, membership grades can indicate a degree of "belonging to the set"; in our approach these are the degree to which every crisp location belongs to the fuzzy region (membership grades in fuzzy set theory can have other interpretations7 as well, but these are not needed for the modelling of fuzzy regions). While modelling a fuzzy region as described provides a more accurate model of a real world situation, it does require many operators from the geographic realm to be extended and also new operators (mainly from the fuzzy realm) to be added at the object level. In this paper, from the GIS realm, the calculation of the surface area and the minimum bounding rectangle for fuzzy regions are considered; from the fuzzy realm the calculation of the α-cut is considered. Other operations (i.e. convex hull of a fuzzy region, distance between two fuzzy regions, …) are still under development.

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

“…approach (see also [49]) and the plateau approach proposed in this article show conceptual resemblance. But the goal of the Spatial Plateau Algebra is to leverage available crisp spatial (vector) data types and the operations defined on them as they can be found in spatial databases.…”

A Quantitative Approach to Topology for Fuzzy Regions

“…It also generalizes the topology for crisp regions: assigning points inside the region the membership grade 1, and points outside the crisp region membership grade 0, the fuzzy methodology results in the classical 9-intersection model. The methodology has been illustrated using our theoretical model, but is equally applicable on the models for implementation purposes we derived from this model ( [8], [9]). …”

Higher Reasoning with Level-2 Fuzzy Regions

“…To consider the complexity of the operators, first more practical models should be derived. This is currently in progress, and we are working on similar approaches as for the simple fuzzy regions: these were approximated using triangular networks or bitmaps ( [5], [11], [12]). The same representation can be used for the candidate fuzzy regions, in which case the complexity depends on both the representation methods uses and the number of candidate regions involved.…”