基于一种新的核函数的模糊粗糙集

Fuzzy Rough Sets Based on New Kernel Functions

模糊粗糙集作为模糊集与粗糙集的结合体,能够有效处理数据的复杂性和不确定性。由模糊相似关系产生的模糊粒结构可以对模糊粗糙集中不确定性的概念进行近似。核函数和模糊相似关系分别是机器学习和模糊粗糙集的核心因素,因此借助模糊相似关系和核函数之间的关系,构造了一种新的核函数,并定义了相应的核模糊粗糙集。最后通过实例说明新构造的核函数具有一定的推广性。

Fuzzy rough sets,as a combination of fuzzy sets and rough sets,can deal with the complexity and uncertainty of data sets effectively. Fuzzy granule structures derived by fuzzy similarity relations are used to study the quantitative fuzzy rough sets. Kernel functions and fuzzy similarity relations are the key factors of machine learning and fuzzy rough sets. With the relationship between the fuzzy similarity relation and the kernel function,this paper presented a new ap- proach to construct kernel function and gave the corresponding fuzzy rough sets. Moreover, this paper gave a compara- tive experimental analysis, and the results show that the new kernel function has generality.