基于最优相似度三支决策的模糊粗糙集模型

Fuzzy Rough Set Model Based on Three-way Decisions of Optimal Similar Degrees

模糊信息系统中,对象的相似度往往会受噪声影响,且它在模型运算中常常并非全部需要高精度参与计算。文中首先引入阈值对(α,β),提出了一种基于相似度三支决策的模糊粗糙集模型;其次利用模糊集近似的三支决策方法,给出了对象相似度三支决策的错误率、决策代价以及相应的语义解释;然后以总体决策代价最小化为目标,给出了最优(α,β)的计算方法,从而建立了一种基于最优相似度三支决策的模糊粗糙集模型;最后通过实例分析说明了该模型的可行性和合理性。本文建立的三支决策模糊粗糙集模型保留了模糊信息系统的不确定性,一定程度地去除了噪声影响,且能通过计算得到最优阈值(α,β),从而建立基于相似度三支决策的最优模型,这将有益于模糊信息系统的应用。

In the fuzzy information system,the noises tend to affect objects’similarity,as well as not all the objects’similar degree need high accuracy for calculation in the model.Consequently,a fuzzy rough set model based on three-way decisions of similar degrees was proposed by introducing thresholds(α,β)in this paper.Then error rates,decision costs and corresponding semantics explanations of three-way decision about objects’similar degrees were given through the three-way decisions method of fuzzy sets approximation.Furthermore,by taking minimizing overall decision costs as the goal,a calculating method of the optimal thresholds(α,β)was given.Therefore,a fuzzy rough sets model based on the three-way decision of optimal similar degrees was established.Finally,an example was analyzed to show the feasibility and reasonability of the model.The fuzzy rough sets model based on three-way decision keeps uncertainty of fuzzy information system,but also reduces noise effects in some extents,and the optimal(α,β)can be got by calculating.This study is benefit for application of the fuzzy information system.