On the perimeter and area of fuzzy sets
Fuzzy Sets and Systems
A general approach to parameter evaluation in fuzzy digital pictures
Pattern Recognition Letters
Fuzzy geometry in image analysis
Fuzzy Sets and Systems
Fuzzy plane geometry I: points and lines
Fuzzy Sets and Systems
Fuzzy plane geometry II: circles and polygons
Fuzzy Sets and Systems
Metric operations on fuzzy spatial objects in databases
Proceedings of the 8th ACM international symposium on Advances in geographic information systems
A spatial model for complex objects with a broad boundary supporting queries on uncertain data
Data & Knowledge Engineering
High-Precision Boundary Length Estimation by Utilizing Gray-Level Information
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometry of Spatial Bipolar Fuzzy Sets Based on Bipolar Fuzzy Numbers and Mathematical Morphology
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Qualified topological relations between spatial objects with possible vague shape
International Journal of Geographical Information Science
Type-2 Fuzzy Logic: Theory and Applications
Type-2 Fuzzy Logic: Theory and Applications
Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology
Information Sciences: an International Journal
Type-2 Fuzzy Logic: A Historical View
IEEE Computational Intelligence Magazine
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Fuzzy geographical phenomena widely exist in the real world, and many modeling and measurement methods for such phenomena have been reported. The most common models and methods are based on type-I fuzzy sets; therefore, they cannot measure the uncertainty of the membership value or describe complicated fuzzy geographical phenomena. Several researchers have used high-order fuzzy theory to avoid the limitations of traditional methods; however, only a few successful models and methods in that domain exist. A fuzzy region model based on interval type-II fuzzy sets is proposed in this paper, considering the uncertainty due to error and to scale effects. Two concepts are proposed to describe the spatial geometric properties of interval type-II fuzzy geographical regions: the geometric summary property and the geometric detailed property, which can reflect different aspects of spatial attributes. Next, some geometric attributes, the area, perimeter, height, width, and extrinsic diameter, of interval type-II fuzzy regions are discussed. The theories and methods proposed in this paper can objectively describe complicated and vague geographical phenomena and thus are meaningful for the development of fuzzy geographical information science.