Research On Matrix Approaches For Local Weighted Neighborhood-based Multigranulation Rough Sets

Since the appearance of Pawlak’s rough set model,numerous researchers have explored and improved it,promoting the wide application of rough set models in the fields of machine learning and data mining.To deal with numerical multi-granularity data and data with unbalanced quality of granularity,researchers have proposed neighborhood multigranulation rough set and weighted multigranulation rough set models,which broaden the application scope of multigranulation rough set.However,with the increasing complexity and size of data,traditional rough set models are unable to handle noisy data and lack computational efficiency.While using matrix algorithms to compute the approximation operators can improve computational efficiency,but its space complexity remains relatively high.Therefore,the research on the rough set models with improved inscription ability and higher computational efficiency has theoretical significance and practical applications.This paper proposes a local weighted neighborhood multigranulation rough sets model and its matrix computing method.The local rough set model is combined with matrix calculation to reduce the time and space complexity of the algorithms for the neighborhood multigranulation rough set.Firstly,this paper defines the variable neighborhood from the perspective of enhancing the flexibility of the neighborhood,and discusses the local weighted neighborhood multigranulation rough sets model and its properties.Then,matrix algorithms are designed to calculate the positive,negative,and boundary domains.However,the local weighted neighborhood multigranulation rough sets model is still time-consuming when the data changes dynamically.Therefore,this paper proposes dynamic updating algorithms for the local weighted neighborhood multigranulation rough sets when the universe and attributes change.Finally,experimental verification demonstrates that the dynamic algorithms are more time-efficient than the static algorithms.The main works involved are presented in the following:(1)This paper proposes a variable neighborhood that is more suitable for the multigranulation rough sets model,building upon the traditional neighborhood concept.It introduces the weighted neighborhood multigranulation rough sets model and the local weighted neighborhood multigranulation rough sets model under variable neighborhoods.The properties of these two models and their interrelationships are thoroughly investigated.Furthermore,these models are redefined using matrix theory,and methods for rapidly computing the variable neighborhood relation matrix from the neighborhood relation matrix and quickly calculating the local variable neighborhood relation matrix from the local neighborhood relation matrix are explored.Additionally,matrix algorithms are designed to compute the positive,negative,and boundary domains.The time complexity of the matrix algorithms is theoretically analyzed,and the effectiveness and stability of the local algorithm are experimentally validated.(2)In order to further enhance computational efficiency,this paper explores dynamic updating algorithms for the local weighted neighborhood multigranulation rough sets model.It focuses primarily on dynamic updating algorithms for scenarios involving changes in objects and attributes.These dynamic matrix algorithms provide methods for updating the local neighborhood relation matrix,local variable neighborhood relation matrix,and other related matrices.The effectiveness of the proposed dynamic algorithms is verified through numerical experiments.