决策蕴含简化算法研究

Simplification of Implication on Decision-Making

摘要: 随着形式背景中数据的增多，概念数量会急剧增加，会使决策的过程变得复杂。大多数参考文献的研究主要集中于给定决策背景的条件下，决策规则的提取，本文首次以决策蕴含简化方法为研究重点，利用计算机模拟人的思维过程，通过计算对象的覆盖，进而计算出决策背景，并在此基础上生成非冗余限制决策蕴含，与非冗余决策规则相比，其形式更简化，更有利于决策者进行决策；其次，为使决策过程简单，提出了决策背景的生成定理及非冗余限制决策蕴含的处理定理并予以证明；随后提出了算法并讨论了算法的时间复杂度。通过实例分析，对比了其它决策规则提取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。最后进行了总结并讨论了开放性问题。

Abstract: As the size of data table grows, the concepts generated become larger in number, which make de-cision-making more complex. The majority of references focused on acquisition of decision rules based on decision formal context which was given. This paper focuses on simplification of implication on decision-making for the first time, makes use of computer simulating the procedures of human thought, via computing the covers of object set, computes decision formal context, which forms the basis of this paper, non-redundant limitary decision implication with more simplified form is deduced compared to decision rules meanwhile, which is beneficial to decision makers; secondly, puts forward judging theorems of handling redundant limitary decision implications and generating decision formal context with demonstration in order to make decision-making simplified; subsequently, proposes an algorithm and discusses the time complexity. Comparing with other algorithms on runtime and ability of classification, experimental results show that the proposed method approves feasibility and accuracy. In the end, it draws a conclusion and discusses open issues.