Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Sorites paradox and vague geographies
Fuzzy Sets and Systems - Special issue on Uncertainty in geographic information systems and spatial data
Type 2 fuzzy sets: an appraisal of theory and applications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Foundations of Fuzzy Systems
Improved Modeling of Elevation Error with Geostatistics
Geoinformatica
Fuzzy Modeling with Spatial Information for Geographic Problems
Fuzzy Modeling with Spatial Information for Geographic Problems
IEEE Transactions on Fuzzy Systems
Multi-scale and multi-criteria mapping of mountain peaks as fuzzy entities
International Journal of Geographical Information Science
Multivariate modeling and type-2 fuzzy sets
Fuzzy Sets and Systems
Uncertainty in ecosystem mapping by remote sensing
Computers & Geosciences
Topological relation analysis between high-order fuzzy regions based on fuzzy logic
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Geometric properties of interval type-II fuzzy regions
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Fuzzy set theory has been suggested as a means for representing vague spatial phenomena, and is widely known for directly addressing some of the issues of vagueness such as the sorites paradox. Higher order vagueness is widely considered a necessary component of any theory of vagueness, but it is not so well known that it too is competently modelled by Type n Fuzzy sets. In this paper we explore the fuzzy representation of higher order vagueness with respect to spatial phenomena. Initially we relate the arguments on philosophical vagueness to Type n Fuzzy sets. As an example, we move on to an empirical generation of spatial Type 2 Fuzzy sets examining the spatial extent of mountain peaks in Scotland. We show that the Type 2 Fuzzy sets can be populated by using alternative parameterisations of a peak detection algorithm. Further ambiguities could also be explored using other parameters of this and other algorithms. We show some novel answers to interrogations of the mountain peaks of Scotland. The conclusion of this work is that higher order vagueness can be populated for Type 2 and higher fuzzy sets. It does not follow that it is always necessary to examine these higher order uncertainties, but a possible advantage in terms of the results of spatial inquiry is demonstrated.