An approach to reasoning topological relations between areal objects under randomness

This paper describes the geometric and statistical properties of areal object under randomness. In order to describe formally such a uncertain topological relation, a new formal model (i. e. 4ID model) is proposed. On the basis of this, the effects of positional uncertainty on topological relations between areal objects are investigated in detail. Some possibility function for the determination of relations are constructed based on the assumption that, randomness of point location complies with a normal distribution, and the concept of uncertain sets of topological relations under randomness is introduced.