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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.

Modeling and manipulating fuzzy regions: strategies to define the topological relation between two fuzzy regions

Schmitz A., Morris A.

Control and Cybernetics

2006

Vol. 35, no 1

73-95

Topological relations between geographic objects are among the most important kinds of relations to manage in Geographic Information Systems (GIS). However, it its very expensive in storage space to keep these relations explicitly stored. Therefore, the relations are usually not directly stored, but they are inferred from the geometry of the objects. Furthermore, the inference of the topological relations is very expensive in processing time, especially when managing complex geographic objects such as fuzzy regions, or regions with multiple alpha-cuts. In this paper we argue that the topological relations between two regions with multiple alpha-cuts can be defined using the topological relations between the crisp regions that compose these two regions. In addition, we present strategies to define the topological relation between two regions with multiple alpha-cuts, with the intent to minimize the number of overlays of crisp regions to be executed to define the topological relationship between the two regions.