粗糙拟阵若干关键问题研究

Big data brings not only big opportunity, but also big challenge. Uncertainty and granularity are essential issues in big data. Rough set is a successful technique for dealing with uncertainty and granularity in data. In order to better use rough set, many scholars have investigated the combination of rough set and matroid, and established abstract structures of of rough set from the viewpoint of matroid. Especially, the applicant has proposed the concept of rough matroid to integrate rough set and matroid into one object. The main characteristic of rough matroid is that it is neither a matroid nor a rough set, but it embeds elements of rough set and matroid into a new object. It is a promising direction for applying rough set and matroid to real life issues. However, rough matroid has only a fundamental frame. It needs to study in detail in order to apply it to practical problems. In this project, we will investigate rough matroid from five aspects, such as representations of the concepts of rough matroid, the axiomatic systems of rough matroid, the relationships between all kinds of special matroids and rough matroid, the connections between different kinds of greedoids and rough matroid, and the greedy algorithms of rough matroid. The output of this research is expected to offer an efficient and practical method for data mining and other fields.

大数据带来大机会，也带来大挑战。不确定性和颗粒性就是大数据中迫切需要解决的问题。粗糙集为不确定性和颗粒性提供了一种解决的途径，已经有许多成功的应用。为了更好地使用粗糙集这个方法，近年来，许多学者对粗糙集和拟阵的结合进行了深入的研究，从更高的角度建立粗糙集的抽象结构。特别地，申请人等提出了粗糙拟阵，试图把粗糙集与拟阵融合成一体。粗糙拟阵的主要特点在于，既不是拟阵，又不是粗糙集，却嵌入了拟阵和粗糙集的双重元素，为粗糙集更广泛的应用提供了一个新的思路。目前，对粗糙拟阵的研究只有一个框架和少量结果。要将粗糙拟阵应用到实际问题中去，还需要对它进行详细的研究。本项目将围绕着粗糙拟阵的概念表示、粗糙拟阵的公理系统、粗糙拟阵和各类特殊拟阵间的联系、粗糙拟阵和各类广义拟阵间的联系以及粗糙拟阵的贪婪算法这五个内容展开。项目的成果有望为数据挖掘等领域提供一个高效而实用的方法。

大数据带来大机会，也带来大挑战。不确定性和颗粒性就是大数据中迫切需要解决的问题。粗糙集为不确定性和颗粒性提供了一种解决的途径，已经有许多成功的应用。为了更好地使用粗糙集这个方法，近年来，许多学者对粗糙集和拟阵的结合进行了深入的研究，从更高的角度建立粗糙集的抽象结构。本项目对粗糙拟阵进行系统的研究，从而更好地融合粗糙集和拟阵的优势。同时将研究成果很好地应用于这二者中的重要问题，如粗糙集中的属性约简和规则提取，拟阵中的贪婪算法设计。继而将这些研究成果应用到分类和聚类等实际问题中去。本项目的研究成果发表了30篇SCI检索的高水平学术论文，推动本学科领域的发展。通过这个项目培养了12位硕士毕业生，1位博士研究生。项目的成果有望为数据挖掘等领域提供一个高效而实用的方法。