基于模糊积分的多模糊决策树融合

给定一个模糊信息系统，可能找到多个重要的模糊属性子集，而且这些重要的模糊属性子集对决策有不同的贡献，会产生不同的影响.如果仅选择其中一个模糊属性子集进行决策，即使是最重要的一个，也会丢失隐含在其他重要的模糊属性子集中的可用信息。为了充分利用模糊信息系统中每个重要的模糊属性子集所提供的信息，提出了一种基于模糊积分的多模糊决策树融合方法.这种方法分3个步骤：1)通过模糊等价关系找到几个重要的模糊属性子集；2)对每个模糊属性子集，利用模糊ID3算法生成一棵模糊决策树；3)用模糊积分融合几棵模糊决策树。实验结果证明了用多模糊决策树融合方法比单模糊决策树分类效果更好。

Given a fuzzy information system, several important fuzzy attribute subsets can be found and each of them can have different contributions to decision-making. If only one of the fuzzy attribute subsets, which may be the most important one, is selected to induce decision rules, some useful information hidden in other important subsets for the decision-making will be lost unavoidably. To sufficiently make use of the information provided by every individual important fuzzy attribute subset in a fuzzy information system, a novel integration of multiple fuzzy decision trees is proposed. The method consists of three stages. First, several important fuzzy attribute subsets are found by fuzzy equivalent relation, and then a fuzzy decision tree for each important fuzzy attribute subset is generated using fuzzy ID3. The fuzzy integral is finally used as a fusion tool to integrate the generated decision trees, which combines together all outputs of the multiple fuzzy decision trees and forms the final decision result. An illustration is given to show the proposed fusion scheme. A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual important fuzzy attribute subset.