In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the ...In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.展开更多
For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft...For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation.In this paper,we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion.In particular,we focus on the quality of the approximation and the computational cost.Based on the bang-bang control principle,a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system.An inner approximation and an outer approximation of the reachable set for the system can be obtained.We prove that the approximation quality measured in Hausdorff distance can be guaranteed.The method is easy to implement and has low computational cost.Finally,the effectiveness of the algorithm is demonstrated by experimental simulation.展开更多
The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi...The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.展开更多
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any ele...We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.60473037,60483081,40275034,60204001,60133010(国家自然科学基金)the China Postdoctoral Science Foundation under Grant No.2003034505(中国博士后科学基金)the open research program of the Geological Processes and Mineral Resources(GPMR),China University of Geosciences under Grant No.GPMR200618(中国地质大学地质过程与矿产资源国家重点实验室开放课题)
基金Supported by the National Natural Science Foundation of China(11171308,61379018,51305400)
文摘In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the （fuzzy） relation in some generalized rough set model. Our results show that by using the axiomatic approach, the （fuzzy） relation determined by （fuzzy） approximation operators is unique in some （fuzzy） double-universe model.
基金partially supported by the National Natural Science Foundation of China(No.12071025)the Natural Science Foundation of Guangdong Province,China(No.2022A1515011172)+1 种基金the Science and Technology on Space Intelligent Control Laboratory for National Defense,China(No.KGJZDSYS-2018-13)the Scientific and Technological Innovation of Shunde Graduate School of University of Science and Technology Beijing,China(No.BK20AE004)。
文摘For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation.In this paper,we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion.In particular,we focus on the quality of the approximation and the computational cost.Based on the bang-bang control principle,a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system.An inner approximation and an outer approximation of the reachable set for the system can be obtained.We prove that the approximation quality measured in Hausdorff distance can be guaranteed.The method is easy to implement and has low computational cost.Finally,the effectiveness of the algorithm is demonstrated by experimental simulation.
文摘The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.
文摘We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X
