中文摘要：

随着形式背景中数据的增多,概念数量会急剧增加。基于决策形式背景的属性约简在保持决策规则分类能力不变的前提下,寻找极小属性子集,使得决策规则得以简化。文章首先将规则分为强规则与弱规则,提出非冗余规则的判定定理及规则约简的判定定理并予以证明;其次提出规则约简及规则输出算法,具体做法是：生成非冗余规则,然后对非冗余规则进行约简,保留规则中相对必要属性的最简形式,删除规则中的不必要属性;随后讨论了算法的时间复杂度。通过实例分析,对比了其他属性约简算法的运行效率和分类能力,证明本文提出的算法具有可行性和正确性。

英文摘要：

As the size of data table grows, the concepts generated become larger in number. Attribute reduction based on decision formal context is to find out minimum subsets of attributes under the precondition of maintaining the ability of classification, rules simplified as well. This paper classifies rules into strong rules and weak rules, puts forward judging theorems of non-redundant rules and rule reduction with demonstration;moreover, proposes an algorithm of rule reduction and output. Non-redundant rules are generated, and then non-redundant rules are reduced to retain the simplest form of relative necessary at- tributes and unnecessary attributes are deleted. Time complexity is also discussed. Comparing with other algorithms on runtime and ability of classification, the experimental results show that the proposed method approves feasibility and accuracy.