On standard models of fuzzy region connection calculus

  • Authors:

  • Weiming Liu;Sanjiang Li

  • Affiliations:

  • Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia;Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2011

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Abstract

The Region Connection Calculus (RCC) is perhaps the most influential topological relation calculus. Based on the first-order logic, the RCC, however, does not fully meet the needs of applications where the vagueness of entities or relations is important and not ignorable. This paper introduces standard models for the fuzzy region connection calculus (RCC) proposed by Schockaert et al. (2008) [18]. Each of such a standard fuzzy RCC model is induced by a standard RCC model in a natural way. We prove that each standard fuzzy RCC model is canonical in the sense that any satisfiable set of fuzzy RCC8 constraints have a solution in it. A polynomial realization algorithm is also provided. As a side product, we show similar sets of fuzzy constraints have similar solutions if both are satisfiable. This allows us to approximate fuzzy RCC constraints that have arbitrary bounds by those have bounds with finite precision.