Spatial Data Types for Heterogeneously Structured Fuzzy Spatial Collections and Compositions.

Fuzzy set theory has found increasing interest in the geosciences, geographic information systems, and spatial database systems to represent geometric objects in the two-dimensional space that reveal an intrinsically vague or fuzzy nature. A spatial object is fuzzy if it contains locations that cannot be assigned completely to the object or to its complement. From a conceptual perspective, fuzzy spatial data types for 0-dimensional fuzzy points, 1-dimensional fuzzy lines, and 2-dimensional fuzzy regions in the plane have been introduced, e.g., by the authors formal Fuzzy Spatial Algebra (FUSA). But the limitation of fuzzy spatial objects to a fixed geometric dimension turns out to be sometimes too restrictive since such objects could benefit from a characterization in terms of several fuzzy spatial sub-objects of different dimensions. An example is a river that consists of 1-dimensional linear parts and 2-dimensional areal parts. For this purpose, this paper introduces a new fuzzy spatial composition type with corresponding operations. It allows one to accommodate fuzzy spatial sub-objects that are either adjacent or disjoint. As a generalization of this type, this paper provides a fuzzy spatial collection type with corresponding operations. Fuzzy collection objects allow one to keep an arbitrary, finite number of fuzzy spatial objects of possibly different dimensions without any topological constraints in a single object. Application examples show how these new data types can be deployed.