Study on the Uncertain Directional Relations Model Based on Cloud Model

The directional relationship of spatial objects is an important spatial relationship of GIS, which is involved in spatial database query, spatial position, and spatial analysis etc. The directional relations in GIS are most commonly represented with qualitative representation model and quantitative representation model. The quantitative models represent direction relationships by angle (quadrant angle or azimuth), while the qualitative models use ordered classes. Traditional models of directional relations define a certain class of direction relationships between spatial objects in the basis of the concepts of the directional relations, such as A is east of B. These methods ignored the uncertainty of directional relations concepts. Based on the analysis of this uncertainty, this paper proposes a new directional relation model based on cloud model, which can availably represent the uncertainty of directional relations concepts. This model expresses the uncertain directional relations through calculating the subjection degree to the four cloud-models of basic directions, and provides a new more reasonable and correct method to analyze the directional relationships. Furthermore, it is an uncertainty conversion model between qualitative directional relation concepts and quantitative directional relation numerical values. * Corresponding author. This is useful to know for communication with the appropriate person in cases with more than one author. 1. INTREDUCTION As one sort of the important spatial relations, directional relations are tightly related to the spatial query and spatial reasoning. Generally, all of the current ways, which include cone-based model, 2D-String model, the models based on MBR (Minimum Bounding Rectangle), etc, describe direction relations based on the exact sorts of qualitative directional relations that the direction relations is represented with a certain directional sort in the final result. However, the description of directional relations in the fuzzy area between two basic directions is uncertain, thus leads to hard description for uncertain relations in precision with conventional models. Cloud model is a quality-quantity interchangeable model combining traditional fuzzy mathematics and probability statistics and realized the conversion between qualitative words and quantitative values (LI Deyi etc, 1995). A planar cloud model was used to describe the uncertainty of the directional relations by DI Kaichang(DI Kaichang, 2001), but there are no models and detail descriptions of directional relations based on the cloud model yet. Based on the cloud model and the traditional descriptions of directional relations, this paper concentrates on the uncertainty of the definition of directional relations and proposes a new cloud model of direction relations, which represents the uncertainty of directions by the certainty degree of the basic direction. Based on this model, we discuss how to express the directional relations between different kinds of reference object and kinds of primary object. To demonstrate the soundness of the model, some examples are given, and the advantages are discussed in the end. 2. ANALYSIS THE TRADITIONAL MODELS OF DIRECTIONAL RELATIONS Early qualitative models for directional relations involve three main categories of cone-based model, projection-based model and Voronoi-based model (XIA Yu etc, 2007). The cone-based model partitions the space by using lines with an origin angle α (Fig. 1). Typical models include 4-direction model (Fig.1 (a)), 8-direction model (Fig.1 (b)) and triangle model (Fig.1 (c)). Such models get the exact definition of the directional relations in the case of point reference object, whereas may give misleading directional relations when reference objects are line and polygon. (a) (b) (c) Figure 1. Cone-based model The projection-based model partitions the space by using lines parallel to the axes (Fig. 2a) (Spiros Skiadopoulos etc, 2007). The commonly used models include MBR model (Fig. 2b), 2Dstring model (Fig. 2c), etc. The MBR model is prominent among these models. It expresses the directional relations by the relations between the MBR of the reference object A and the primary object B. It intuitively partitions the plane around