By analyzing direction relation representation model in two-dimension space,this paper proposes a direction relation qualitative representation and reasoning model in three-dimension space,which is the extension of direction relation matrix model on the plane.

By relating direction-relation matrix,representing direction relations,to the extended 9-intersection model,describing topological relations,three approaches are presented to derive topological relations from direction relations between regions with broad boundaries.

According to the features of Xi\'an actual map data,a spatial direction query based on direction-relation matrix model was designed and developed,and the experimental result was satisfying.

So, those publications adopted the signals of different frequency to build the DOA estimation model of incoherent signals but the same center frequency in its directional matrix.

Deduces the fuzzy relation matrixes from the definitions of the membership functions in various states.

On the basis of the above definitions,we construct an undirected graph model for product family architecture and its customization constraint relation matrix.

The relationship matrix between user requirements and technological characteristics determined by designers in the quality room reflected objectively the degree of importance of user s requirements to a certain extent.

With "capacity, safety, productivity and investment" as feature targets, and according to three different levels of hump automation, the author constructs the fuzzy relationship matrix,finds the fuzzy subset, and according to which, makes comprehensive evaluation with figures.