Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificati...Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.展开更多
The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to de...The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.展开更多
In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel fu...In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.展开更多
文摘Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.
文摘The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.
文摘In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.
