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Advances in Fuzzy Systems
Volume 2012, Article ID 167939, 15 pages
Research Article

Two-Dimensional Fuzzy Spatial Relations: A New Way of Computing and Representation

Mathematics, Image, and Applications (MIA) Laboratory, University of La Rochelle, 17000 La Rochelle, France

Received 8 August 2011; Revised 19 December 2011; Accepted 6 January 2012

Academic Editor: Erich Klement

Copyright © 2012 Nadeem Salamat and El-hadi Zahzah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Fuzziness is found everywhere, in modeling spatial relations, fuzziness is found at object level as well as in relation semantics. Commonly, fuzzy topological relations are computed between fuzzy objects. Fuzziness in relation semantics is represented by fuzzy topological relations between crisp objects and these types of fuzzy topological relations are much less developed. In this paper, we propose a method for combining fuzzy topological and directional relations. We also propose an algorithm for defuzzification of relations which provides us a binary topological and directional relation between a 2D object pair. These relations are represented in a neighborhood graph. For validation and assessment, a number of experiments have been performed on artificial data.