Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method fo...Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.展开更多
A Furstenberg family $\mathcal{F}$ is a family, consisting of some subsets of the set of positive integers, which is hereditary upwards, i.e. A ? B and A ∈ $\mathcal{F}$ imply B ∈ $\mathcal{F}$ . For a given system ...A Furstenberg family $\mathcal{F}$ is a family, consisting of some subsets of the set of positive integers, which is hereditary upwards, i.e. A ? B and A ∈ $\mathcal{F}$ imply B ∈ $\mathcal{F}$ . For a given system (i.e., a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family $\mathcal{F}$ , the definition of $\mathcal{F}$ -scrambled pairs of points in the space has been given, which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be $\mathcal{F}$ -scrambled pairs corresponding respectively to suitable Furstenberg family $\mathcal{F}$ . In the present paper we explore the basic properties of the set of $\mathcal{F}$ -scrambled pairs of a system. The generically $\mathcal{F}$ -chaotic system and the generically strongly $\mathcal{F}$ -chaotic system are defined. A criterion for a generically strongly $\mathcal{F}$ -chaotic system is showed.展开更多
Assessment of debris flow hazards is important for developing measures to mitigate the loss of life and property and to minimize environmental damage. Two modified uncertainty models, Set Pair Analysis （SPA） and mod...Assessment of debris flow hazards is important for developing measures to mitigate the loss of life and property and to minimize environmental damage. Two modified uncertainty models, Set Pair Analysis （SPA） and modified Set Pair Analysis （mSPA）, were suggested to assess the regional debris flow hazard. A ease study was conducted in seven towns of the Beichuan county, Sichuan Province, China, to test and compare the application of these two models in debris flow hazard assessment. The results showed that mSPA only can fit for value-variables, but not for non value-variable assessment indexes, Furthermore, as for a given assessment index xi, mSPA only considers two cases, namely, when grade value increases with xi and when grade value decreases with xi. Thus, mSPA can not be used for debris flow hazard assessment but SPA is credible for the assessment because there are no limitations when using SPA model to assess the debris flow hazard. Therefore, in this study SPA is proposed for assessing debris flow hazard.展开更多
Spectra and tilings play an important role in analysis and geometry respectively.The relations between spectra and tilings have bafied the mathematicians for a long time.Many conjectures,such as the Fuglede conjecture...Spectra and tilings play an important role in analysis and geometry respectively.The relations between spectra and tilings have bafied the mathematicians for a long time.Many conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired results.In the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.展开更多
In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomi...In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.展开更多
There are many problems in Social Internet of Things(IoTs),such as complex topology information,different degree of association between nodes and overlapping communities.The idea of set pair information grain computin...There are many problems in Social Internet of Things(IoTs),such as complex topology information,different degree of association between nodes and overlapping communities.The idea of set pair information grain computing and clustering is introduced to solve the above problems so as to accurately describe the similarity between nodes and fully explore the multi-community structure.A Set Pair Three-Way Overlapping Community Discovery Algorithm for Weighted Social Internet of Things(WSIoT-SPTOCD)is proposed.In the local network structure,which fully considers the topological information between nodes,the set pair connection degree is used to analyze the identity,difference and reverse of neighbor nodes.The similarity degree of different neighbor nodes is defined from network edge weight and node degree,and the similarity measurement method of set pair between nodes based on the local information structure is proposed.According to the number of nodes'neighbors and the connection degree of adjacent edges,the clustering intensity of nodes is defined,and an improved algorithm for initial value selection of k-means is proposed.The nodes are allocated according to the set pair similarity between nodes and different communities.Three-way community structures composed of a positive domain,boundary domain and negative domain are generated iteratively.Next,the overlapping node set is generated according to the calculation results of community node membership.Finally,experiments are carried out on artificial networks and real networks.The results show that WSIoT-SPTOCD performs well in terms of standardized mutual information,overlapping community modularity and F1.展开更多
An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal...An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal identity degree based on relative positive region is proposed so that the identity degree can be computed in an objective method without any preliminary or additional information about data, which is consistent with the notion of objectivity in rough set theory and data mining theory. Subsequently, an algorithm is proposed, and in two examples, the global optimum identity degree is found out. Finally, in regard to optimum connection degree, the method of rules extraction for connection degree rough set model based on generalization function is presented by which the rules extracted from a decision table are enumerated.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51209032, 50779005)
文摘Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10471049)
文摘A Furstenberg family $\mathcal{F}$ is a family, consisting of some subsets of the set of positive integers, which is hereditary upwards, i.e. A ? B and A ∈ $\mathcal{F}$ imply B ∈ $\mathcal{F}$ . For a given system (i.e., a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family $\mathcal{F}$ , the definition of $\mathcal{F}$ -scrambled pairs of points in the space has been given, which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be $\mathcal{F}$ -scrambled pairs corresponding respectively to suitable Furstenberg family $\mathcal{F}$ . In the present paper we explore the basic properties of the set of $\mathcal{F}$ -scrambled pairs of a system. The generically $\mathcal{F}$ -chaotic system and the generically strongly $\mathcal{F}$ -chaotic system are defined. A criterion for a generically strongly $\mathcal{F}$ -chaotic system is showed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51279116)the New Teacher Fund of Ministry of Education of China (Grant No. 20120181120124)+1 种基金the Excellent Scholar Fund of Sichuan UniversityOpen Fund Program of State key Laboratory of Hydraulics and River Engineering, Sichuan University, China (Grant No. 0901)
文摘Assessment of debris flow hazards is important for developing measures to mitigate the loss of life and property and to minimize environmental damage. Two modified uncertainty models, Set Pair Analysis （SPA） and modified Set Pair Analysis （mSPA）, were suggested to assess the regional debris flow hazard. A ease study was conducted in seven towns of the Beichuan county, Sichuan Province, China, to test and compare the application of these two models in debris flow hazard assessment. The results showed that mSPA only can fit for value-variables, but not for non value-variable assessment indexes, Furthermore, as for a given assessment index xi, mSPA only considers two cases, namely, when grade value increases with xi and when grade value decreases with xi. Thus, mSPA can not be used for debris flow hazard assessment but SPA is credible for the assessment because there are no limitations when using SPA model to assess the debris flow hazard. Therefore, in this study SPA is proposed for assessing debris flow hazard.
基金supported by the Key Project of Chinese Ministry of Education (Grant No.108117)National Natural Science Foundation of China (Grant No.10871123)
文摘Spectra and tilings play an important role in analysis and geometry respectively.The relations between spectra and tilings have bafied the mathematicians for a long time.Many conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired results.In the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.
基金supported partially by the National Natural Science Foundation of China under Grant Nos.11771034 and 11401018
文摘In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.
文摘There are many problems in Social Internet of Things(IoTs),such as complex topology information,different degree of association between nodes and overlapping communities.The idea of set pair information grain computing and clustering is introduced to solve the above problems so as to accurately describe the similarity between nodes and fully explore the multi-community structure.A Set Pair Three-Way Overlapping Community Discovery Algorithm for Weighted Social Internet of Things(WSIoT-SPTOCD)is proposed.In the local network structure,which fully considers the topological information between nodes,the set pair connection degree is used to analyze the identity,difference and reverse of neighbor nodes.The similarity degree of different neighbor nodes is defined from network edge weight and node degree,and the similarity measurement method of set pair between nodes based on the local information structure is proposed.According to the number of nodes'neighbors and the connection degree of adjacent edges,the clustering intensity of nodes is defined,and an improved algorithm for initial value selection of k-means is proposed.The nodes are allocated according to the set pair similarity between nodes and different communities.Three-way community structures composed of a positive domain,boundary domain and negative domain are generated iteratively.Next,the overlapping node set is generated according to the calculation results of community node membership.Finally,experiments are carried out on artificial networks and real networks.The results show that WSIoT-SPTOCD performs well in terms of standardized mutual information,overlapping community modularity and F1.
基金supported by the National Natural Science Foundation of China (70571032)
文摘An improvement of tolerance relation is proposed in regard to rough set model based on connection degree by which reflexivity of relation can be assured without loss of information. Then, a method to determine optimal identity degree based on relative positive region is proposed so that the identity degree can be computed in an objective method without any preliminary or additional information about data, which is consistent with the notion of objectivity in rough set theory and data mining theory. Subsequently, an algorithm is proposed, and in two examples, the global optimum identity degree is found out. Finally, in regard to optimum connection degree, the method of rules extraction for connection degree rough set model based on generalization function is presented by which the rules extracted from a decision table are enumerated.
