Spatial Reasoning with Integrated Qualitative-Metric Fuzzy Constraint Networks

Qualitative Spatial Reasoning can be greatly improved if metric information can be represented and reasoning can be performed on it; moreover, modelling vagueness and uncertainty in both qualitative and metric relations allows reasoning in a more flexible way about data coming from real world. In this paper Rectangle Algebra is integrated with a bi-dimensional Point Algebra by defining a set of 25 Point-Region relations, in this way a Spatial Qualitative Algebra (SQA) among point and regions is obtained. Besides, SQA is extended to deal with uncertain data by means of the Fuzzy Sets Theory. Fuzzy metric information is represented using pyramidal possibility distributions, and transformation functions that allow passing from qualitative to metric information and vice versa are provided.