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Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable 被引量:5
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作者 Yang Weifang Yan Haowen Li Jonathan 《Geodesy and Geodynamics》 2015年第2期113-125,共13页
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
关键词 Spatial similarity degree Map generalization Map scale change Point clouds Quantitative description Spatial similarity relations Multi-scale map spaces Curve fitting method
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Rough similarity degree and rough close degree in rough fuzzy sets and the applications
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作者 Li Jian Xu Xiaojing Shi Kaiquan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期945-951,共7页
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
关键词 rough fuzzy set rough similarity degree rough close degree CLUSTERING recognition of rough pattern maximal similarity degree principle.
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Static rough similarity degree and its applications
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作者 Xu Xiaojing Li Jian Shi Kaiquan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第2期311-315,共5页
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
关键词 rough similarity degree CLUSTERING recognition of rough pattern maximal similarity degree principle.
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A New Definition of Intuitionistic Fuzzy Similarity Degree
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作者 Qun Liu Changhuan Feng 《Open Journal of Statistics》 2016年第1期31-36,共6页
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
关键词 Intuitionistic Fuzzy Sets similarity degree Fuzzy similarity Matrix Clustering Analysis
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APPROACH FOR FUZZY MULTI-ATTRIBUTE DECISION-MAKING WITH FUZZY COMPLEMENTARY PREFERENCE RELATION ON ALTERNATIVES 被引量:2
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作者 周宏安 刘三阳 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2007年第1期74-79,共6页
In presented fuzzy multi-attribute decision-making (FMADM) problems, the information about attribute weights is interval numbers and the decision maker (DM) has fuzzy complementary preference relation on alternati... In presented fuzzy multi-attribute decision-making (FMADM) problems, the information about attribute weights is interval numbers and the decision maker (DM) has fuzzy complementary preference relation on alternatives. Firstly, the decision-making information based on the subjective preference information in the form of the fuzzy complementary judgment matrix is uniform by using a translation function. Then an objective programming model is established. Attribute weights are obtained by solving the model, thus the fuzzy overall values of alternatives are derived by using the additive weighting method. Secondly, the ranking approach of alternatives is proposed based on the degree of similarity between the fuzzy positive ideal solution of alternatives (FPISA) and the fuzzy overall values. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible. It is easy to be operated and implemented on a computer. Finally, the proposed method is applied to the project evaluation in the venture investment. 展开更多
关键词 fuzzy multi-attribute decision-making objective programming WEIGHT similarity degree PRIORITY
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Approach of fault diagnosis based on similarity degree matching distance function 被引量:3
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作者 WANG RiXin JIN Yang XU MinQiang 《Science China(Technological Sciences)》 SCIE EI CAS 2013年第11期2709-2720,共12页
A new diagnosis method based on the similarity degree matching distance function is proposed.This method solves the problem that the traditional fault diagnosis methods based on transition system model cannot deal wit... A new diagnosis method based on the similarity degree matching distance function is proposed.This method solves the problem that the traditional fault diagnosis methods based on transition system model cannot deal with the"special state"which cannot match the target states completely.For evaluating the relationship between the observation and the target states,this paper first defines a new distance function based on the viewpoint of energy to measure the distance between two attribute values.After that,all the distances of the attributes in the state vector are used to synthesize the distance between two states.For calculating the similarity degree between two states,a trend evaluation method is developed.It analyzes the main direction of the trend of the state transfer according to the distances between the observation and each target state and their historical records.Applying the diagnosis method to a primary power subsystem of a satellite,the simulation result shows that it is effective. 展开更多
关键词 fault diagnosis similarity degree matching measurement-scale distance function trend evaluation
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Similarity Degrees for the Crossed Product of von Neumann Algebras
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作者 Jin Song WU Wen Ming WU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第5期723-736,共14页
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
关键词 similarity degree von Neumann algebra weakly compact action compact action crossed product
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A Weak* Similarity Degree Characterization for Injective von Neumann Algebras
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作者 Zhe DONG Ya Fei ZHAO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第10期1689-1697,共9页
In this note, we show that avon Neumann algebra M is injective if and only if the weak* similarity degree d.(M) ≤ 2.
关键词 Weak* similarity degree injective von Neumann algebra operator space
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Theory of truth degrees of propositions in the logic system Ln^* 被引量:21
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作者 LI Jun1,2 & WANG Guojun1,3 1. Institute of Mathematics, Shaanxi Normal University, Xi’an 710062, China 2. School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China 3. Research Center for Science, Xi’an Jiaotong University, Xi’an 710049, China 《Science in China(Series F)》 2006年第4期471-483,共13页
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
关键词 truth degree similarity degree approximate reasoning.
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Theory of (n) truth degrees of formulas in modal logic and a consistency theorem 被引量:13
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作者 WANG GuoJun DUAN QiaoLin 《Science in China(Series F)》 2009年第1期70-83,共14页
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
关键词 modal logic (n) truth degrees consistency theorem temporal logic (n) modality similarity degrees (n) modality logic metric space approximate reasoning
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On Some Problems Studied by R. V. Kadison
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作者 ErikCHRISTENSEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第3期523-534,共12页
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
关键词 Keywords von Neumann algebra Property Γ similarity degree Length INJECTIVITY Complete boundedness DERIVATIONS Hochschild cohomology
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