【摘要】 模糊ID3算法处理的对象是具有模糊条件属性和模糊决策属性的模糊决策表,它利用平均模糊分类熵作为启发式选择扩展属性,利用模糊置信度作为叶子结点的终止条件.当用模糊ID3算法处理连续值和离散值决策表时,需要对连续值或离散值条件属性进行模糊化.模糊化的关键是模糊测度的确定,但确定合适的模糊测度非常困难,而且模糊化会损失有用的信息.针对这些问题,基于粗糙模糊集技术,提出了一种模糊决策树归纳算法,称为粗糙模糊决策树(RFDT:Rough Fuzzy Decision Tree).RFDT可直接处理离散值模糊决策表,归纳模糊决策树,不需要模糊化的过程.和模糊ID3算法类似,RFDT也分为三步:(1)利用粗糙模糊依赖度作为启发式选择扩展属性;(2)用选择的扩展属性划分样例集合;(3)如果划分的样例集合满足终止条件,则算法终止;否则递归地重复步骤(1)和(2).提出的算法用Kosko模糊熵作为叶子结点的终止条件,并通过一个例子说明了模糊决策树的归纳过程.更多还原

【Abstract】 The fuzzy ID3 is tailored for inducing fuzzy decision trees from the fuzzy decision tables with fuzzy condition attributes and fuzzy decision attribute.In fuzzy ID3,average fuzzy classification entropy is used as heuristic for selecting the expanded attributes,while fuzzy confidence degree is used as termination conditions of leaf nodes.When fuzzy ID3 is applied to decision tables with continuous-valued or discrete-valued conditional attributes,it is necessary for fuzzy ID3 to fuzzify the continuous-valued or discrete-valued conditional attributes.The key issue of fuzzification is to determine the fuzzy measures,but it is very difficult to determine the suitable fuzzy measure.Furthermore,the fuzzification will result in losing useful information.In order to deal with these problems,based on the rough fuzzy set technique,an induction algorithm of fuzzy decision trees named rough fuzzy decision tree(RFDT)is proposed in this paper,RFDT can directly deal with the decision tables with discrete-valued conditional attributes,and induce fuzzy decision trees without fuzzification.Similar to fuzzy ID3,RFDT also consists of three steps:(1)Select expanded attributes with rough fuzzy dependence;(2)Partition the set of instances with the selected expanded attributes;(3)Ifthe terminal condition of the proposed algorithm is satisfied,then the algorithm is terminated.Otherwise,repeat the step(2)and(3)iteratively.The proposed algorithm RFDT use Kosko fuzzy entropy as termination condition of leaf nodes,an example is presented to illustrate the induction process of fuzzy decision tree.更多还原