Abstract: Ranking method is an important part of multi-granulation rough set. The advantages and disadvantages of the currently existing ranking method of multi-granularity rough set in dominance relation are analyzed. The existing sorting formula is improved to make that the structure of the advantage matrix satisfies the complementary symmetry and overcomes the problem of failure effectively. At the same time, a new method on account of the relative dominance degree is proposed for multi-granularity rough set based on dominance relation. The weighted ranking formula of multi-granularity rough set based on dominance relation has been defined, with the importance of different granularity considered. The paper even discusses the meaning and nature of the formula. Finally, the experimental results show the feasibility and effectiveness of the two methods.

Key words: dominance relation, multi-granularity rough set, ranking method

摘要： 排序方法是多粒度粗糙集研究的一个重要内容。分析了现有优势关系多粒度粗糙集排序方法的优缺点，对现有排序公式进行改进，使其构造的优势关系矩阵满足对称互补性，且能有效克服方法失效问题。同时，基于相对优势度的视角提出优势关系多粒度粗糙集排序新方法；考虑不同粒度的重要性问题，定义了优势关系多粒度粗糙集的加权排序公式，讨论了公式的含义与性质；最后实例说明了两种方法的实用性和有效性。

关键词: 优势关系, 多粒度粗糙集, 排序方法