Heuristic Method to Attribute Reduction for Decision Region Distribution Preservation

DOI：10.13328/j.cnki.jos.004507

 作者 单位 E-mail 马希骜 西南交通大学 信息科学与技术学院, 四川 成都 610031 王国胤 计算智能重庆市重点实验室（重庆邮电大学）, 重庆 400065 wanggy@ieee.org 于洪 计算智能重庆市重点实验室（重庆邮电大学）, 重庆 400065

在决策粗糙集中，由于引入了概率阈值，属性增加或减少时，正域或者非负域有可能变大、变小或者不变，即属性的增减与决策域（正域或非负域）之间不再具有单调性.分析结果表明，现有的基于整个决策域的属性约简定义可能会改变决策域.为使决策域保持不变，引入了正域分布保持约简与非负域分布保持约简的概念.此外，决策域的非单调性使得属性约简算法必须检查一个属性集合的所有子集.为了简化算法设计，提出了正域和非负域分布条件信息量的定义，并证明其满足单调性，从而为设计决策域分布保持约简的启发式计算方法提供了理论基础.为了进一步获得最小约简，提出一种基于遗传算法的决策域分布保持启发式约简算法，并在两种单调的决策域分布条件信息量基础上构造了新算子，即修正算子，确保遗传算法找到的是约简而不是约简的超集.对比实验从分类正确率与误分类代价两个方面都反映了决策域分布保持约简定义的合理性，并且，所提出的遗传算法在大多数情况下都找到了最小约简.

In decision-theoretic rough set models, since decision regions (positive region or non-negative region) are defined by allowing some extent of misclassification, the monotonicity of decision regions with respect to attribute sets does not hold. The definition of attribute reduction based on the whole decision regions may change decision regions. In order not to change decision regions, the positive region and non-negative distribution preservation reduction are introduced into decision-theoretic rough set models. Moreover, due to the non-monotonicity of decision regions, attribute reduction algorithms must search all possible subsets of an attribute set. The positive region and non-negative region distribution condition information contents are presented to facilitate the design of heuristic algorithms for decision region distribution preservation reduction. In a bid to then solve the minimum attribute reduction problem, heuristic genetic algorithm is applied to decision region distribution preservation reduction. A new modify operator is constructed by using two kinds of decision region distribution condition information contents so that genetic algorithm can find decision region distribution preservation reduction. Experimental results verify the effectiveness of decision region distribution preservation reduction and show the efficiency of the genetic algorithm to solve the minimum attribute reduction problem.
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