属性约简是粗糙集理论研究最广泛的一个问题，目前在粗糙集属性约简算法方面研究存在着一些不足，比如，大多数约简算法都存在着时间复杂度高、只能处理静态数据等情况。本文以经典粗糙集模型为出发点，以各属性之间的依赖度为启发信息对数据集提出了求解约简的高效算法，具体内容如下：

首先，在传统的基于依赖度约简算法中，不同的属性集在约简过程中起的作用大小不同，如果遍历整个属性集合之间的依赖度势必会造成时间和空间上的浪费。本文在将等价关系下的依赖度方法扩展到属性集合之间的相互依赖度基础上，提出了一种依赖度排序约简算法，该算法只保留对约简的必要属性集。实例对比分析表明：改进后的算法能有效地去除冗余属性，从而获得相对较优的约简结果。

其次，针对经典的基于属性重要度的约简方法在约简过程中仅仅考虑到单个属性之间的重要性，而忽略了各属性之间的相关性可能会导致约简结果不完备的情况，将信息论中的互信息引入算法中用来度量各条件属性的相关性，在此基础上提出了一种最优依赖度约简算法。通过对6个经典数据集在约简后属性数量、约简精度两方面对比实验，实验结果表明，新算法充分考虑到了各属性之间相关性，约简结果更为完备。

最后，针对传统的约简算法大多只能处理静态数据的不足，将属性间相对依赖度作为启发信息，融入动态三支决策计算模型，以动态数据集中单样本增加为基础，证明了样本增加三支区域更新机制，提出了一种基于相对依赖度的三支决策增量属性约简算法。通过案例分析以及UCI数据实验验证表明：在复杂动态的大数据环境中，改进算法比经典非增量三支决策约简算法具有更低的时间复杂度和更高的约简效率，同时算法也具备较强的稳健性和和有效性。

Attribute reduction is the most in-depth problem of rough set theory. At present, there are deficiencies in the research of attribute reduction algorithms of rough set. For example, most reduction algorithms have high time complexity and can only deal with static data. Taking the classical rough set model as the starting point and the dependency between attributes as the heuristic information, this paper proposes an efficient algorithm for solving and reducing the data set. The specific contents are as follows:

Firstly, in the traditional dependency based reduction algorithm, different attribute sets play different roles in the reduction process. If the dependency between the whole attribute set is traversed, it is bound to cause a waste of time and space. On the basis of extending the dependency method under equivalence relationship to the interdependence between attribute sets, this paper proposes a dependency ranking reduction algorithm, which only retains the necessary attribute sets for reduction. The comparative analysis of examples shows that the improved algorithm can effectively remove redundant attributes and obtain relatively better reduction results.

Secondly, aiming at the situation that the classical reduction method based on attribute importance only considers the importance of a single attribute in the reduction process and ignores the correlation between attributes, which may lead to incomplete reduction results, the mutual information in information theory is introduced into the algorithm to measure the correlation of conditional attributes. On this basis, an optimal dependency reduction algorithm is proposed. The experimental results show that the new algorithm fully considers the correlation between attributes, and the reduction results are more complete.

Finally, in view of the deficiency that most traditional reduction algorithms can only deal with static data, the relative dependency between attributes is used as heuristic information and integrated into the dynamic three way decision calculation model. Based on the increase of single sample in the dynamic data set, the three way regional update mechanism of sample increase is proved, and a three branch decision incremental attribute reduction algorithm based on relative dependency is proposed. The case analysis and UCI data experimental verification show that in the complex and dynamic big data environment, the improved algorithm has lower time complexity and higher reduction efficiency than the classical non incremental three way decision reduction algorithm. At the same time, the algorithm also has strong robustness and effectiveness.

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