三支决策是知识获取和数据挖掘的有效工具之一, 运用分而治之的思想将论域划分为三个论域子空间并分别采取不同的策略, 可以有效的解决不确定不完整的信息. 随着信息形式的多样化复杂化多粒化, 发展出动态的三支决策方法序贯三支决策, 通过一种循序渐进多步骤的方式对不确定信息从较粗的粒度向更细粒度进行挖掘, 并在不同的粒度级别下设置不同的决策代价. 现有模型更多是主观的设置粒层的阈值, 因此会忽略粒层中可被分类的等价类, 使得模型效率降低并且适用性较差. 针对该问题本文围绕基于粒计算的序贯三支决策展开研究, 主要研究内容如下.

现有序贯三支决策阈值设置不灵活且实际适用性差, 提出一种数据驱动多粒序贯三支分类模型, 首先结合等价类的重要度与候选比例函数得到代价函数矩阵, 从而获得数据驱动阈值序列. 其次证明了阈值的适用性, 并且结合等价类的更新状态降低算法的时间复杂度. 最后给出实例说明分类算法流程, 选取不同的数据集与现有的序贯三支决策方法进行比较, 数值实验表明该模型可以提高准确率的同时保证较好的运算效率, 提高了决策的科学性和合理性.

多粒层相较于单粒层优势明显, 因此基于所提出的数据驱动多粒序贯三支决策模型给出相适应的属性约简算法. 首先根据已有代价结构定义了一种新的基于粒度容量的决策过程代价以及决策结果代价, 并设计了全局代价结构, 给出了基于该全局代价的属性约简算法. 其次给出结合序贯过程的属性约简方法, 可有效减少后续粒层需要计算的属性个数. 实验结果表明该方法的有效性, 并且可以降低后续粒层的算法时间复杂度, 给出可调节的多粒序贯三支决策属性约简结果.

Three-way decision rough sets are one of the effective tools for knowledge acquisition and data mining. It uses the thought of divide and rule to divide the universe into three subspaces of the universe and adopts different strategies. This granularity based approach can effectively address uncertain and incomplete information. Based on the diversity and complexity of granular information forms, it has evolved into a dynamic three-way decisions method which calls sequential three-way decisions, it utilizes a multi-step approach to mine uncertain information from coarse to fine granularity, and sets different decisions costs at different granularity levels. The existing model is more subjective when setting the threshold of the granular layer, so it will ignore the equivalence class that can be classified in the granular layer, which reduces the efficiency of the model and is not applicable. This paper focuses on the sequential three-way decisions based on granular computing. The main research contents are as follows.

The existing threshold setting of Sequential three-way decisions rough set is not flexible and has poor practical applicability. Mode of data-driven sequential three-way decisions classification based on granular computing is proposed. Firstly, the cost function matrix is obtained by combining the significance of the equivalence class and the candidate proportion function, and then the data-driven threshold sequence is obtained. Secondly, the applicability of the threshold is proved, and the time complexity of the algorithm is reduced by combining the update state of the equivalent class. Finally, an example is given to illustrate the classification algorithm flow, and different UCI data sets are selected to compare with the existing sequential three-way decisions method. Numerical experiments show that the model has better accuracy, higher operating efficiency and more scientific and reasonable decisions-making.

Compared to single granularity hierarchical structures, multi granularity hierarchical structures have significant advantages. Therefore, this article proposes an adaptive attribute reduction algorithm based on the proposed data-driven multi-granularity sequential three-way decisions model. Firstly, based on the existing cost structure, a new decisions process cost based on granularity and a new decisions result cost were defined, so a global cost structure was designed. And then provide attribute reduction algorithms based on this global cost. Secondly, it provides how to effectively reduce the number of attributes that need to be calculated by combining sequential process attribute reduction methods. The experimental results demonstrate the effectiveness of this method, which can reduce the algorithm time complexity of subsequent granularity layers, and provide attribute reduction results for multi-granularity sequential three-way decisions.