基于互信息率的广义多尺度决策表的最优尺度组合选择

Optimal Scale Combination Selection of Generalized Multi-Scale Decision Tables Based on Mutual Information Rate

多尺度信息表是一类特殊的具有分层递阶的数据集,这类数据集研究的一个重要问题是根据最终决策保持某种性质的最优尺度组合的选择.文章通过利用香农熵,研究在广义多尺度决策表中保证在“互信息量满足需求的前提下,互信息率最大”的最优尺度组合选择问题.首先,介绍信息表中的熵和互信息量的概念及其性质,综合考虑“提供足够多的信息”与“降低对运算和存储的需求”这两个因素,定义互信息率,并通过研究互信息率的性质说明定义的合理性.其次,通过引入参数给出广义多尺度决策表中基于互信息率的最优尺度组合概念,使决策者可以通过调整参数满足自己的偏好,并给出计算最优尺度组合的算法.最后,通过与最新的研究方法比较,说明文章提出新方法的有效性,并且,此方法无需判断决策表的协调性,都可以找到它基于互信息率的最优尺度组合.

Multi-scale information table is a special kind of hierarchical data set.An important issue in such a data set is to select optimal scale combination in order to keep certain condition for final decision.In this paper,shannon entropy is used to study the optimal scale combination selection problem in the generalized multi-scale decision table to ensure the "maximum mutual information rate under the premise that the mutual information meets the requirements".Firstly,we introduce the concents and properties of entropy and mutual information in the information table,and define the mutual information rate by considering the two factors of "providing enough information" and "reducing the demand for operation and storage",and explain the rationality of the definition by studying the nature of the mutual information rate.Secondly,the concept of optimal scale combination based on mutual information rate in generalized multi-scale decision table is given by introducing a parameter,so that decision-makers can adjust the parameter to meet their own preferences,and the algorithm to calculate the optimal scale combination is given.Finally,the effectiveness of the new method is illustrated by comparing with the latest research method,moreover,this method can find its optimal scale combination based on mutual information rate without judging the consistency of decision table.