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Deriving topological concepts for fuzzy regions: from properties to definitions

Verstraete J.

Control and Cybernetics

2012

Vol. 41, no. 1

113-143

Fuzzy regions are a concept allowing the uncertain or imprecise spatial data to be represented. Many geographic or spatial data are prone to uncertainty or imprecision and while such data can be represented, it is still necessary to be able to perform basic tasks one expects to perform in a geographic context. A number of operations have been considered in the past; in this contribution the topological concepts of fuzzy regions will be examined. For this purpose, appropriate definitions for the boundary, interior and exterior of fuzzy regions will be developed. These definitions can then be applied in an extension of the 9-intersection model.

Fuzzy regions: interpretations of surface area and distance

Verstraete J.

Control and Cybernetics

2009

Vol. 38, no 2

509-526

This contribution concerns the modelling of fuzzy information in geographic databases. For this purpose, fuzzy regions and fuzzy points have been defined in the past, along with a number of suitable operations. For numerical information - such as the surface area of fuzzy regions, or the distance between fuzzy regions and/or fuzzy points - the computation depends on the interpretation given to the fuzzy regions or points. Consequently, it is important to differentiate between the interpretation in order to obtain correct results. This article explains in detail the impact of the interpretation in terms of both the surface area and the distance.

Bitmap based structures for the modeling of fuzzy entities

Verstraete J., Tre G. de, Hallez A.

Control and Cybernetics

2006

Vol. 35, no 1

147-164

Bitmap models are a known technique to model field based geographic information. Commonly, geographic information is modelled in a crisp sense, even though in reality it most likely is an approximation. In this article, we present the use of bitmap based structures to model imprecise or uncertain locations and ditto regions: these structures should be considered to be extensions of respectively a point and a polygon. The imprecission or uncertainty is modelled using fuzzy set theory. Apart from presenting the structures, appropriate operators are denned and explained.