We discuss the set of all Boolean association rules. By defining special partial order on the set, we get an isomorphism between the set and a special finite ranked poset. Through discussing some basic properties of the finite ranked poset, we can clearly represent the hierarchical structure of all Boolean association rules. Meanwhile, the Hasse diagram of the poset offers a visualization view of the structure.
Cohen-Sutherland clipping algorithm may produce the invalid intersection points, which will reduce the efficiency of the whole algorithm. To avoid the shortcoming, this paper has put forward an improved algorithm based on Cohen-Sutherland algorithm. Given a line segment, by the coordinate values of clipping window vertexes and the implicit equation of the line segment, the improved algorithm can rapidly judge which clipping window edge has real intersection point(s) with the line segment. Experiments show that the improved algorithm is more efficient than other improved Cohen-Sutherland algorithms in reference papers.
This paper examines the problem of weak ratio rules between nonnegative real-valued data in a transactional database. The weak ratio rule is a weaker form than Flip Korn's ratio rule. After analyzing the mathematical model of weak ratio rules problem, the authors conclude that it is a generalization of Boolean association rules problem and every weak ratio rule is supported by a Boolean association rule. Following the properties of weak ratio rules, the authors propose an algorithm for mining an important subset of weak ratio rules and construct a weak ratio rule uncertainty reasoning method. An example is given to show how to apply weak ratio rules to reconstruct lost data, and forecast and detect outliers.
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