基于三层粒结构的三支邻域熵

Three-way Neighborhood Entropies Based on Three layer Granular Structures

邻域粗糙集在实际应用中具有灵活性,相关的邻域信息度量在不确定性分析和知识发现中具有重要作用.经典的条件邻域熵具有相交不完备性和非层次性.对条件邻域熵进行扩展改进,建立了基于三层粒结构的三支邻域熵.首先,提出三支概率,研究三支概率的系统性和单调性;然后,利用三支概率函数及层次构建思想,提出基于三层粒结构的三支邻域熵,并获得系统性、单调性/非单调性;最后,利用实例和实验对以上相关度量的关系、性质进行验证.结果表明提出的三支邻域熵扩展和丰富了条件邻域熵.

The neighborhood rough sets have flexibility in practical application.The relevant neighborhood information measures play an important role in uncertainty analysis and knowledge discovery.The classical conditional neighborhood entropy has intersection incompleteness and non-hierarchy.In this paper,three-way neighborhood entropies based on three-layer granular structures are established,which expand and improve classical conditional neighborhood entropy.Firstly,three-way probabilities are acquired,and the systematicness and monotonicity of three-way probabilities are studied.Then,by using the three-way probabilities function and three-layer granular structures,we construct three-way neighborhood entropies based on three-layer granular structures,and obtain some systematicness,monotonicity/nonmonotonicity.Finally,the relevant properties and mutual relationships are also effectively verified by a decision table and one experiment.The results show that three-way neighborhood entropies expand and enrich conditional neighborhood entropy.