A probabilistic paradigm for handling uncertain objects in GIS by randomized graph algebra

Wen Zhong Shi, H.Y. Wu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Probability theory faces difficulties when it is applied to describing uncertain objects in geographic information system (GIS). This is mainly due to the fact that an object in GIS is normally described by a series of discrete vertexes. Modeling uncertainty objects should be therefore based on error of the composed vertexes. This type of model is normally complex and relatively difficult to implement because of many unknown factors, such as the number of vertexes of a polygon, error nature of each individual vertex and error correlation among the vertexes. In this paper, a probabilistic paradigm for handling uncertain objects in GIS by randomized graph algebra is presented. The theoretical basis for this paradigm is the randomized graph algebra-a probability theory for graph-which is newly proposed in this study. Classical probability theory is based on numerical algebra and is also an extension of numerical algebra by further defining probability density within a numerical domain. In the same token, this study begins with defining graph algebra as the basis for probability theory for graph. First, we adopt the theory of graph algebra and further refine the theory by defining the modulo operation for graph. As a result, a graph can thereafter be treated as a "number" and operated by "addition", "subtraction" and others. Second, we construct a measure space by generating sigma-algebra and defining measurable function upon it. The measure space becomes a probability space when the measurable function is a probability density function. Third, we propose the probabilistic paradigm for describing and inferring the uncertainty of geometric objects in GIS by applying the developed randomized graph algebra.
Original language English 648-657 10 Progress in Natural Science 13 9 https://doi.org/10.1080/10020070312331344190 Published - 2003

Keywords

• GIS
• Uncertain objects
• Graph algebra
• Measure space

ASJC Scopus subject areas

• Materials Science(all)