模糊相似关系下变精度模糊粗糙集

Fuzzy similarity relation based variable precision fuzzy rough sets

经典变精度模糊粗糙集模型是基于模糊等价关系建立的.在实际应用中,模糊等价关系很难直接构造,需要通过求模糊相似关系的传递闭包生成.对模糊关系的这种改造会丢失较多有价值的信息,而且还增大了模糊粗糙集应用的计算复杂度.基于模糊逻辑算子构造2个模糊集的相对错误包含度,构造性地提出基于模糊相似关系的变精度模糊粗糙集模型,研究了该模型的性质.该模型一方面具有变精度粗糙集的优点,对噪声数据具有很好的容错能力,另一方面是基于模糊相似关系建立的,其应用范围更为广泛.

A classical variable precision fuzzy rough set was built on the basis of fuzzy equivalent relationships. Nonetheless, it is hard to directly obtain the fuzzy equivalent relationships, which are usually replaced by a closure of fuzzy equivalent relationships, and this method causes a loss of much valuable information and increases the computation complexity in the application of the fuzzy rough set. This paper first took advantage of a fuzzy logical operator to construct fuzzy relative error rates of classification, and then proposed a variable precision fuzzy rough set model based on fuzzy similarity relationships. Moreover, the properties of this model were investigated. On the one hand, the model is able to deal with noise data with the advantages of variable precision rough sets; on the other hand, since it is based on fuzzy similarity relationships, the model could be applied more widely.