Equality in Approximate Tolerance Geometry

  • Gwendolin WilkeEmail author
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 322)


The framework of Approximate Tolerance Geometry (ATG) has been proposed in [1] as an approach to handling large and heterogeneous imperfections in geometric data in vector-based geographic information systems. Here, different types of positional error can often only be subsumed as possibilistic location constraints. The application of the ATG framework to a classical geometry provides a calculus for the propagation of this error type in geometric reasoning. As a first step towards an implementation of an ATG geometry, the paper applies the framework to the geometric equality relation. It thereby lays the basis for the application of ATG to the other axioms of classical geometry.


geographic information system fuzzy geometry uncertain points fuzzy logic with evaluated syntax rational Pavelka logic Łukasiewicz logic fuzzy similarity relation fuzzy equivalence relation 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Information ScienceUniversity of Applied Sciences and Arts Northwestern SwitzerlandOltenSwitzerland

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