基于模糊度的决策树生成算法
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摘要
在处理不确定问题中,生成模糊决策树是一种常用的方法.其算法主要包含2个步骤,一个是树的生成条件,主要是确定扩展属性的选择标准,并以此为核心得到生成模糊决策树的启发式算法.另一个则是树的终止条件,否则会造成树的过度拟合的情况.目前,典型的算法中通常利用粗糙模糊依赖度作为选择扩展属性的依据,但是这个依赖函数不具备单调性,从而导致算法有不收敛的可能,基于这个问题,给出了模糊度的定义,重新定义了模糊依赖度和模糊粗糙度,选择模糊依赖度最大的条件属性作为根结点;然后,使用模糊粗糙度作为叶子结点的终止条件;最后,通过实例说明了整个模糊决策树的归纳过程.
In dealing with uncertain problems, generating the fuzzy decision tree is a common method. This generation algorithm mainly consists of two steps. One is the generating condition of the fuzzy decision tree, whose main purpose is to determine the criteria for selecting extended attributes and to get the heuristic algorithm. The other one is the termination condition of the fuzzy decision tree, and otherwise it will cause the over-fitting of the fuzzy decision tree. At present, the typical algorithms often use rough-fuzzy dependence as a basis for the choice of extended attributes, but this dependence function does not possess monotonicity, leading to possible non-convergence. For solving this problem, the paper redefines the fuzzy dependency and roughness, chooses the condition attribute as a root node with the maximum fuzzy dependence, using fuzzy roughness as a leaf node termination condition. Finally, the induction process of the whole fuzzy decision tree is illustrated by an example.
In dealing with uncertain problems, generating the fuzzy decision tree is a common method. This generation algorithm mainly consists of two steps. One is the generating condition of the fuzzy decision tree, whose main purpose is to determine the criteria for selecting extended attributes and to get the heuristic algorithm. The other one is the termination condition of the fuzzy decision tree, and otherwise it will cause the over-fitting of the fuzzy decision tree. At present, the typical algorithms often use rough-fuzzy dependence as a basis for the choice of extended attributes, but this dependence function does not possess monotonicity, leading to possible non-convergence. For solving this problem, the paper redefines the fuzzy dependency and roughness, chooses the condition attribute as a root node with the maximum fuzzy dependence, using fuzzy roughness as a leaf node termination condition. Finally, the induction process of the whole fuzzy decision tree is illustrated by an example.
引文
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[7] PAWLAK Z,SOWINSKI R.Rough set approach to multi-attribute decision analysis[J].European Journal of Operational Research,1994,72(3):443-459.
[8] 张小红,裴道武,代建华.模糊数学与Rough集理论[M].北京:清华大学出版社,2013:222-226.
[9] 陈良莉,黄天民.一种基于属性加权综合直觉梯形摸糊数多属性决策方法[J].西南民族大学学报(自然科学版),2017,43(1):76-81.
[10] 陈德刚.模糊粗糙集理论与方法[M].北京:科学出版社,2013:110-117.
[11] 王熙照,翟俊海.基于不确定性的决策树归纳[M].北京:科学出版社,2012:247-255.
[12] ZHAI J H .Fuzzy decision tree based on fuzzy-rough technique[J].Soft Computing,2011,15 ( 6 ):1087-1096.
[13] 翟俊海,侯少星,王熙照.粗糙模糊决策树归纳算法[J].南京大学学报,2016,52(2):306-312.
[2] YUAN Y,SHAW M J.Induction of fuzzy decision trees[J].Fuzzy Sets and Systems,1995,69(2):125-139.
[3] WANG X Z,YEUNG D S,TSANG E C C.A comparative study on heuristic algorithms for generating fuzzy decision trees[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B (Cybernetics),2001,31(2):215-226.
[4] MORSI N N,YAKOUT M M.Axiomatics for fuzzy rough sets[J].Fuzzy Sets and Systems,1998,100(1/2/3):327-342.
[5] TSANG E C C,CHEN D,YEUNG D S,et al.Attributes reduction using fuzzy rough sets[J].IEEE Transactions on Fuzzy systems,2008,16(5):1130-1141.
[6] PAWLAK Z.Rough sets [J].International Journal of Information and Computer Science,1982,11(5):341-356.
[7] PAWLAK Z,SOWINSKI R.Rough set approach to multi-attribute decision analysis[J].European Journal of Operational Research,1994,72(3):443-459.
[8] 张小红,裴道武,代建华.模糊数学与Rough集理论[M].北京:清华大学出版社,2013:222-226.
[9] 陈良莉,黄天民.一种基于属性加权综合直觉梯形摸糊数多属性决策方法[J].西南民族大学学报(自然科学版),2017,43(1):76-81.
[10] 陈德刚.模糊粗糙集理论与方法[M].北京:科学出版社,2013:110-117.
[11] 王熙照,翟俊海.基于不确定性的决策树归纳[M].北京:科学出版社,2012:247-255.
[12] ZHAI J H .Fuzzy decision tree based on fuzzy-rough technique[J].Soft Computing,2011,15 ( 6 ):1087-1096.
[13] 翟俊海,侯少星,王熙照.粗糙模糊决策树归纳算法[J].南京大学学报,2016,52(2):306-312.