The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity d...The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.展开更多
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve ...In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.展开更多
Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar ...Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.展开更多
The definition of rough similarity degree is given based on the axiomatic similarity degree, and the properties of rough similarity degree are listed. Using the properties of rough similarity degree, the method of clu...The definition of rough similarity degree is given based on the axiomatic similarity degree, and the properties of rough similarity degree are listed. Using the properties of rough similarity degree, the method of clustering in rough systems can be obtained. After clustering, a new sample can be recognized by the principle of maximal rough similarity degree.展开更多
As far as the problem of intuitionistic fuzzy cluster analysis is concerned, this paper proposes a new formula of similarity degree with attribute weight of each index. We conduct a fuzzy cluster analysis based on the...As far as the problem of intuitionistic fuzzy cluster analysis is concerned, this paper proposes a new formula of similarity degree with attribute weight of each index. We conduct a fuzzy cluster analysis based on the new intuitionistic fuzzy similarity matrix, which is constructed via this new weighted similarity degree method and can be transformed into a fuzzy similarity matrix. Moreover, an example is given to demonstrate the feasibility and validity of this method.展开更多
The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree ...The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.展开更多
By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^* is introdu...By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^* is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.展开更多
Several problems studied by professor R. V. Kadison are shown to be closely related. The problems were originally formulated in the contexts of homomorphisms of C*-algebras, cohomology of von Neumann algebras and pert...Several problems studied by professor R. V. Kadison are shown to be closely related. The problems were originally formulated in the contexts of homomorphisms of C*-algebras, cohomology of von Neumann algebras and perturbations of C*-algebras. Recent research by G. Pisier has demonstrated that all of the problems considered are related to the question of whether all C*-algebras have finite length.展开更多
基金funded by the Natural Science Foundation Committee,China(41364001,41371435)
文摘The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.
基金supported by Chinese Universities Scientific Fund(Grant No.WK0010000031)supported by National Natural Science Foundation of China(Grant Nos.11231390,11371222,11301511)
文摘In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.
基金the Fujian Provincial Natural Science Foundation of China (Z0510492006J0391)
文摘Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.
基金the Fujian Provincial Natural Science Foundation of China (Z051049, 2006J0391).
文摘The definition of rough similarity degree is given based on the axiomatic similarity degree, and the properties of rough similarity degree are listed. Using the properties of rough similarity degree, the method of clustering in rough systems can be obtained. After clustering, a new sample can be recognized by the principle of maximal rough similarity degree.
文摘As far as the problem of intuitionistic fuzzy cluster analysis is concerned, this paper proposes a new formula of similarity degree with attribute weight of each index. We conduct a fuzzy cluster analysis based on the new intuitionistic fuzzy similarity matrix, which is constructed via this new weighted similarity degree method and can be transformed into a fuzzy similarity matrix. Moreover, an example is given to demonstrate the feasibility and validity of this method.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10331010 and 10771129)the Foundation of 211 Constructionof Shaanxi Normal University
文摘The theory of (n) truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the (n) truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of (n) truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of (n) similarity degrees among modal formulas is proposed and the (n) modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.
基金the National Natural Science Foundation of China (Grant No. 10331010), and the Innovation Foundation for Doctors of Shaanxi Normal University.
文摘By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^* is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.
基金Supported by the Zhejiang Qianjiang Talent Program in 2008the Program for New Century Excellent Talents in University of Ministry of Education of China in 2010+1 种基金the National Natural Science Foundation of China(Grant No.11271321)the Fundamental Research Funds of Zhejiang University
文摘In this note, we show that avon Neumann algebra M is injective if and only if the weak* similarity degree d.(M) ≤ 2.
文摘Several problems studied by professor R. V. Kadison are shown to be closely related. The problems were originally formulated in the contexts of homomorphisms of C*-algebras, cohomology of von Neumann algebras and perturbations of C*-algebras. Recent research by G. Pisier has demonstrated that all of the problems considered are related to the question of whether all C*-algebras have finite length.