Attribute reduction through the combined approach of Rough Sets(RS)and algebraic topology is an open research topic with significant potential for applications.Several research works have introduced a strong relations...Attribute reduction through the combined approach of Rough Sets(RS)and algebraic topology is an open research topic with significant potential for applications.Several research works have introduced a strong relationship between RS and topology spaces for the attribute reduction problem.However,the mentioned recent methods followed a strategy to construct a new measure for attribute selection.Meanwhile,the strategy for searching for the reduct is still to select each attribute and gradually add it to the reduct.Consequently,those methods tended to be inefficient for high-dimensional datasets.To overcome these challenges,we use the separability property of Hausdorff topology to quickly identify distinguishable attributes,this approach significantly reduces the time for the attribute filtering stage of the algorithm.In addition,we propose the concept of Hausdorff topological homomorphism to construct candidate reducts,this method significantly reduces the number of candidate reducts for the wrapper stage of the algorithm.These are the two main stages that have the most effect on reducing computing time for the attribute reduction of the proposed algorithm,which we call the Cluster Filter Wrapper algorithm based on Hausdorff Topology.Experimental validation on the UCI Machine Learning Repository Data shows that the proposed method achieves efficiency in both the execution time and the size of the reduct.展开更多
In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the ...In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.展开更多
Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group”...Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group” of Gusi? in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.展开更多
基金funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant Number 102.05-2021.10.
文摘Attribute reduction through the combined approach of Rough Sets(RS)and algebraic topology is an open research topic with significant potential for applications.Several research works have introduced a strong relationship between RS and topology spaces for the attribute reduction problem.However,the mentioned recent methods followed a strategy to construct a new measure for attribute selection.Meanwhile,the strategy for searching for the reduct is still to select each attribute and gradually add it to the reduct.Consequently,those methods tended to be inefficient for high-dimensional datasets.To overcome these challenges,we use the separability property of Hausdorff topology to quickly identify distinguishable attributes,this approach significantly reduces the time for the attribute filtering stage of the algorithm.In addition,we propose the concept of Hausdorff topological homomorphism to construct candidate reducts,this method significantly reduces the number of candidate reducts for the wrapper stage of the algorithm.These are the two main stages that have the most effect on reducing computing time for the attribute reduction of the proposed algorithm,which we call the Cluster Filter Wrapper algorithm based on Hausdorff Topology.Experimental validation on the UCI Machine Learning Repository Data shows that the proposed method achieves efficiency in both the execution time and the size of the reduct.
文摘In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.
基金supported by the Fund of Elitist Development of Beijing (Grant No. 20071D1600600412)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group” of Gusi? in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.
