Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on ...Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.展开更多
A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equival...A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equivalent to Schweizer-Smital chaos occurring on the measure centre.展开更多
The ranks of cyclic and negacyclic codes over the finite chain ring R as well as their minimal generating sets are defined, and then the expression forms we presented by studying the structures of cyclic and negacycli...The ranks of cyclic and negacyclic codes over the finite chain ring R as well as their minimal generating sets are defined, and then the expression forms we presented by studying the structures of cyclic and negacyclic codes over the finite chain ring R. Through the paper, it is assumed that the length of codes n can not be divided by the characteristic of R.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,we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost periodically-forced scalar reaction-diffusion equation:u_(t)=u_(xx)+f(t,u,u_(x)),t>0,0<x<L...In this paper,we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost periodically-forced scalar reaction-diffusion equation:u_(t)=u_(xx)+f(t,u,u_(x)),t>0,0<x<L(0.1)with the periodic boundary condition u(t,0)=u(t,L),u_(x)(t,0)=u_(x)(t,L),(0.2)where f is uniformly almost periodic in t.In particular,we study the topological structure of the limit sets of the skew-product semiflow.It is proved that any compact minimal invariant set(throughout this paper,we refer to it as a minimal set)can be residually embedded into an invariant set of some almost automorphically-forced flow on a circle S^(1)=R/LZ(see Definition 2.4 for“residually embedded”).Particularly,if f(t,u,p)=f(t,u,-p),then the flow on a minimal set can be embedded into an almost periodically-forced minimal flow on R(see Definition 2.4 for“embedded”).Moreover,it is proved that the ω-limit set of any bounded orbit contains at most two minimal sets that cannot be obtained from each other by phase translation.In addition,we further consider the asymptotic dynamics of the skew-product semiflow generated by(0.1)with the Neumann boundary condition u_(x)(t,0)=u_(x)(t,L)=0 or the Dirichlet boundary condition u(t,0)=u(t,L)=0.For such a system,it has been known that theω-limit set of any bounded orbit contains at most two minimal sets.By applying the new results for(0.1)+(0.2),under certain direct assumptions on f,we prove in this paper that the flow on any minimal set of(0.1)with the Neumann boundary condition or the Dirichlet boundary condition can be embedded into an almost periodically-forced minimal flow on R.Finally,a counterexample is given to show that even for quasi-periodically-forced equations,the results we obtain here cannot be further improved in general.展开更多
The study of cyclic codes over rings has generated a lot of public interest.In this paper,we study cyclic codes and their dual codes over the ring Z P2 of length pe,and find a set of generators for these codes.The ran...The study of cyclic codes over rings has generated a lot of public interest.In this paper,we study cyclic codes and their dual codes over the ring Z P2 of length pe,and find a set of generators for these codes.The ranks and minimal generator sets of these codes are studied as well,which play an important role in decoding and determining the distance distribution of codes.展开更多
Causality Diagram (CD) is a new graphical knowledge representation based on probability theory. The application of this methodology in the safety analysis of the gas explosion in collieries was discussed in this paper...Causality Diagram (CD) is a new graphical knowledge representation based on probability theory. The application of this methodology in the safety analysis of the gas explosion in collieries was discussed in this paper, and the Minimal Cut Set, the Minimal Path Set and the Importance were introduced to develop the methodology. These concepts are employed to analyze the influence each event has on the top event ? the gas explosion, so as to find out about the defects of the system and accordingly help to work out the emphasis of the precautionary work and some preventive measures as well. The results of the safety analysis are in accordance with the practical requirements; therefore the preventive measures are certain to work effectively. In brief, according to the research CD is so effective in the safety analysis and the safety assessment that it can be a qualitative and quantitative method to predict the accident as well as offer some effective measures for the investigation, the prevention and the control of the accident.展开更多
文摘Several strategies for the minimal attribute reduction with polynomial time complexity (O(nk)) have been developed in rough set theory. Are they complete? While investigating the attribute reduction strategy based on the discernibility matrix (DM),a counterexample is constructed theoretically, which demonstrates that these strategies are all incomplete with respect to the minimal reduction.
文摘A class of minimal subshifts which display Schweizer-Smital chaos and have zero topotogical entropy is constructed, and it is proved that for a compact system, the positive topological entropy is not generally equivalent to Schweizer-Smital chaos occurring on the measure centre.
基金Partly supported by the National Natural Science Foundations of China (No.60673074)key project of Ministry of Education Science and Technology’s Research (107065).
文摘The ranks of cyclic and negacyclic codes over the finite chain ring R as well as their minimal generating sets are defined, and then the expression forms we presented by studying the structures of cyclic and negacyclic codes over the finite chain ring R. Through the paper, it is assumed that the length of codes n can not be divided by the characteristic of R.
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.
基金supported by National Science Foundation of USA(Grant No.DMS1645673)supported by National Natural Science Foundation of China(Grant Nos.11825106,11771414 and 12090012)+2 种基金Wu Wen-Tsun Key Laboratory of Mathematics,Chinese Academy of Sciences and University of Science and Technology of Chinasupported by National Natural Science Foundation of China(Grant Nos.11971232,12071217 and 11601498)the Chinese Scholarship Council(Grant No.201906845011)for its financial support。
文摘In this paper,we consider the asymptotic dynamics of the skew-product semiflow generated by the following time almost periodically-forced scalar reaction-diffusion equation:u_(t)=u_(xx)+f(t,u,u_(x)),t>0,0<x<L(0.1)with the periodic boundary condition u(t,0)=u(t,L),u_(x)(t,0)=u_(x)(t,L),(0.2)where f is uniformly almost periodic in t.In particular,we study the topological structure of the limit sets of the skew-product semiflow.It is proved that any compact minimal invariant set(throughout this paper,we refer to it as a minimal set)can be residually embedded into an invariant set of some almost automorphically-forced flow on a circle S^(1)=R/LZ(see Definition 2.4 for“residually embedded”).Particularly,if f(t,u,p)=f(t,u,-p),then the flow on a minimal set can be embedded into an almost periodically-forced minimal flow on R(see Definition 2.4 for“embedded”).Moreover,it is proved that the ω-limit set of any bounded orbit contains at most two minimal sets that cannot be obtained from each other by phase translation.In addition,we further consider the asymptotic dynamics of the skew-product semiflow generated by(0.1)with the Neumann boundary condition u_(x)(t,0)=u_(x)(t,L)=0 or the Dirichlet boundary condition u(t,0)=u(t,L)=0.For such a system,it has been known that theω-limit set of any bounded orbit contains at most two minimal sets.By applying the new results for(0.1)+(0.2),under certain direct assumptions on f,we prove in this paper that the flow on any minimal set of(0.1)with the Neumann boundary condition or the Dirichlet boundary condition can be embedded into an almost periodically-forced minimal flow on R.Finally,a counterexample is given to show that even for quasi-periodically-forced equations,the results we obtain here cannot be further improved in general.
基金the National Natural Science Foundation of China(No.60673074)the Key Project of Ministry of Education Science and Technology’s Research(107065)
文摘The study of cyclic codes over rings has generated a lot of public interest.In this paper,we study cyclic codes and their dual codes over the ring Z P2 of length pe,and find a set of generators for these codes.The ranks and minimal generator sets of these codes are studied as well,which play an important role in decoding and determining the distance distribution of codes.
基金Supported by the Natural Science Foundation of China (No. 59677009) the National Research Foundation for the Doctoral Program of Higher Education of China (No.99061116)
文摘Causality Diagram (CD) is a new graphical knowledge representation based on probability theory. The application of this methodology in the safety analysis of the gas explosion in collieries was discussed in this paper, and the Minimal Cut Set, the Minimal Path Set and the Importance were introduced to develop the methodology. These concepts are employed to analyze the influence each event has on the top event ? the gas explosion, so as to find out about the defects of the system and accordingly help to work out the emphasis of the precautionary work and some preventive measures as well. The results of the safety analysis are in accordance with the practical requirements; therefore the preventive measures are certain to work effectively. In brief, according to the research CD is so effective in the safety analysis and the safety assessment that it can be a qualitative and quantitative method to predict the accident as well as offer some effective measures for the investigation, the prevention and the control of the accident.
