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Fuzzy Logic for Incidence Geometry.

Alex Tserkovny1

  • 1Dassault Systemes, 175 Wyman Street, Waltham, MA 02451, USA.

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Summary

This study introduces a mathematical framework for approximate geometric reasoning with extended geographic objects, enhancing geographic information systems (GIS). It enables GIS to process spatial data using fuzzy logic for more human-like reasoning with landmarks and water bodies.

Area of Science:

  • Geographic Information Science
  • Spatial Reasoning
  • Fuzzy Logic Applications

Background:

  • Geographic Information Systems (GIS) currently lack robust geometric reasoning for extended objects.
  • Human spatial reasoning easily handles extended geographic entities, treating them analogously to points.
  • Existing GIS primarily rely on precise Cartesian coordinates, limiting analysis of loosely defined geographic features.

Purpose of the Study:

  • To develop a mathematical framework for approximate geometric reasoning with extended geographic objects.
  • To enable GIS to perform spatial reasoning with complex, real-world geographic entities.
  • To bridge the gap between human spatial cognition and GIS capabilities.

Main Methods:

  • Utilizing fuzzy logic as a reasoning system for the geometry of extended objects.

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  • Fuzzifying axioms of incidence geometry and Euclid's first postulate.
  • Introducing a fuzzy equivalence relation for "extended lines sameness" using fuzzy conditional inference.

    • Main Results:

    • A mathematical apparatus for approximate geometric reasoning with extended objects is presented.
    • Fuzzy logic is demonstrated as a viable system for handling geometric uncertainty in GIS.
    • New concepts of fuzzy "degree of indiscernibility" and "discernibility measure" for extended points are proposed.

    Conclusions:

    • The proposed framework enhances GIS capabilities for approximate geometric reasoning with extended geographic objects.
    • Fuzzy logic provides a powerful tool for integrating human-like spatial reasoning into GIS.
    • This research paves the way for more intuitive and accurate spatial analysis in geography.