Let G be a graph with vertex set V（G） and edge set E（G）. A labeling f ： V（G） →Z2 induces an edge labeling f＊： E（G） → Z2 defined by f＊（xy） = f（x） ＋ f（y）, for each edge xy ∈ E（G）. For i ∈ Z2, le...Let G be a graph with vertex set V（G） and edge set E（G）. A labeling f ： V（G） →Z2 induces an edge labeling f＊： E（G） → Z2 defined by f＊（xy） = f（x） ＋ f（y）, for each edge xy ∈ E（G）. For i ∈ Z2, let vf（i） = ｜{v ∈ V（G） ： f（v） = i}｜ and ef（i） = ｜{e ∈ E（G） ： f＊（e） =i}｜. A labeling f of a graph G is said to be friendly if ｜vf（0）- vf（1）｜ ≤ 1. The friendly index set of the graph G, denoted FI（G）, is defined as {｜ef（0）- ef（1）｜： the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS（n, m）.展开更多
A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and d...A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.展开更多
Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i...Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.展开更多
In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;...In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;d] to exist.展开更多
Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex fri...Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex friendly labeling/induces an edge labeling f*E(G)→Z2,defined by f*(xy)=f(x)+f(y)for each xy∈E(G).Let er(i)=\{e∈E(G):f*(e)=i}|.The full friendly index set of G,denoted by FFI(G),is the set{ef*(1)-ep(0):f is friendly}.In this paper,we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2×Pn.展开更多
In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p an...In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p and High[n]~p and prove that Low [n]~p is Σ~P[n+3]-complete and High [n]~p is Σ~P [n+4]-complete.展开更多
Radar anti-jamming performance evaluation is a necessary link in the process of radar development,introduction and equipment. The applications of generalized rough set theory are proposed and discussed in this paper t...Radar anti-jamming performance evaluation is a necessary link in the process of radar development,introduction and equipment. The applications of generalized rough set theory are proposed and discussed in this paper to address the problems of big data, incomplete data and redundant data in the construction of evaluation index system. Firstly, a mass of real-valued data is converted to some interval-valued data to avoid an unacceptable number of equivalence classes and classification rules, and the interval similarity relation is employed to make classifications of this interval-valued data. Meanwhile, incomplete data can be solved by a new definition of the connection degree tolerance relation for both interval-valued data and single-valued data, which makes a better description of rough set than the traditional limited tolerance relation. Then, E-condition entropy-based heuristic algorithm is applied to making attribute reduction to optimize the evaluation index system, and final decision rules can be extracted for system evaluation. Finally, the feasibility and advantage of the proposed methods are testified by a real example of radar anti-jamming performance evaluation.展开更多
背景消化性溃疡(PUD)是消化系统常见疾病,中医药治疗作为PUD的有效治疗措施,但目前针对中医药治疗PUD的随机对照试验(RCT)中,方法学质量、结局指标的选择等存在较大局限性,给疗效评价、资料整合分析等带来一定挑战。目的本文系统梳理近1...背景消化性溃疡(PUD)是消化系统常见疾病,中医药治疗作为PUD的有效治疗措施,但目前针对中医药治疗PUD的随机对照试验(RCT)中,方法学质量、结局指标的选择等存在较大局限性,给疗效评价、资料整合分析等带来一定挑战。目的本文系统梳理近15年中医药干预PUD的RCT结局指标应用状况与试验设计要点,旨在为构建中医药治疗PUD核心指标集及优化临床试验设计提供参考依据。方法计算机检索中文数据库:中国知网、万方数据知识服务平台、维普网、中国生物医学文献服务系统,以及国际权威数据库:PubMed、Embase、Cochrane Library、Web of Science中关于中医药治疗PUD的RCT文献;检索时限为2010—2024年。对纳入文献进行Cochrane偏倚风险评估,并统计、归纳、分析相关结局指标。结果共纳入323篇RCT文献,34933例患者,单项研究样本量最大为498例,最小为40例,平均样本量为108例;171篇报告中医证型,其中使用频次最高为脾胃虚寒(31篇,18.13%);47篇采用纯中医治疗,276篇采用中西医结合治疗;治疗疗程多为4周(119次,36.84%);结局指标按照功能属性划分为6类,共报道了170种结局指标,总频次为1962次,其中使用频次较高的结局指标是临床总有效率(233次,11.88%)、幽门螺杆菌根除率(165次,8.41%)、不良反应(155次,7.90%);纳入文献偏倚风险评估多数为不明确。结论中医药治疗PUD的RCT尚存在中医辨证分型与疾病分期欠规范、方法学设计(盲法、分配隐藏)待完善、主次结局指标区分不明确、临床疗效标准未统一、结局指标测量时间差距大、中医证候/症状积分评分标准多元化、伦理注册待重视、安全性指标报告不规范等问题。建议积极开展中医药治疗PUD的核心指标集研究,优化完善方法学质量,为中医药治疗PUD的临床实践提供科学性、可靠性、实用性证据。展开更多
为提高可消除项集的挖掘效率,在WPPC-Tree基础上提出优化后开始-结束序列树(start-finish-order tree,SFOTree),定义开始-结束序列集合(start-finish-order-set,SFO-Set)和开始-结束序列集合差(difference of start-finish-orderset,dSF...为提高可消除项集的挖掘效率,在WPPC-Tree基础上提出优化后开始-结束序列树(start-finish-order tree,SFOTree),定义开始-结束序列集合(start-finish-order-set,SFO-Set)和开始-结束序列集合差(difference of start-finish-orderset,dSFO-Set),建立项集的收益索引,提出一种基于dSFO-Set的可消除项集挖掘算法。利用dSFO-Set性质和收益索引,提高项集收益的计算效率,减少可消除项集的挖掘代价。分别在稠密数据集和稀疏模拟数据集上与传统算法进行测试比较,实验结果表明,该算法具有更好的挖掘效率。展开更多
In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition ...In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.展开更多
Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features ma...Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features may be redundant, and others may be irrelevant and noisy. The conventional supervised FS methods evaluate various feature subsets using an evaluation function or metric to select only those features which are related to the decision classes of the data under consideration. However, for many data mining applications, decision class labels are often unknown or incomplete, thus indicating the significance of unsupervised feature selection. However, in unsupervised learning, decision class labels are not provided. In this paper, we propose a new unsupervised quick reduct （QR） algorithm using rough set theory. The quality of the reduced data is measured by the classification performance and it is evaluated using WEKA classifier tool. The method is compared with existing supervised methods and the result demonstrates the efficiency of the proposed algorithm.展开更多
The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference ana...The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.展开更多
The comprehensive evaluation method of enterprise core competitiveness is proposed by combining rough sets and gray correlation theories. Firstly,the initial index is screened through rough set attribute reduction alg...The comprehensive evaluation method of enterprise core competitiveness is proposed by combining rough sets and gray correlation theories. Firstly,the initial index is screened through rough set attribute reduction algorithm,and the evaluation weight of each index is obtained through the rough set theory. Then,based on the gray correlation theory, an evaluation model is built for empirical analysis. The 30 financial institutions on the Yangtze River Delta are examined from the theoretical and empirical perspective.The result demonstrates not only the feasibility of rough set attribute reduction algorithm in the core competitiveness index system of the financial institution,but also the accuracy of the combination of these two methods in the comprehensive evaluation of corporate core competitiveness.展开更多
Field data of outcrop spectrums provide important basis for modeling of hyper-spectral remote sensing aiming at mineral prospecting. We make an approach to the application of rough set theory in spectral discriminatio...Field data of outcrop spectrums provide important basis for modeling of hyper-spectral remote sensing aiming at mineral prospecting. We make an approach to the application of rough set theory in spectral discrimination of rocks. We build a decision table with an adequate number of samples (outcrops) of known rock type (the universe), of which the conditional attributes are discretized 'area spectrum absorption indexes' (ASAI) corresponding to wavelength intervals, and the decision attribute is rock type. We search to obtain the exhaustive set of reducts of the table, each of which will serve as a variable number of deduction rules. Suppose we have n (usually a very big number) rules in total and there are m types of rocks in our universe, for any unknown sample, we judge its rock type by each of those rules. An unknown sample may be recognized as a different type by different rules because it is outside our universe, and we accept the most frequent judgment result and ignore the other m-1 types of results. Our ASAI is an improvement upon the traditional spectrum absorption index (SAI), better applicable to field spectrums: given a spectrum curve and a wavelength interval, we take the average reflectance within the interval as a base line and let ASAI=a below/(a above+a below), where a below and a above stand for total areas, bounded by the curve, the base line and the borders of the intervalbelow and above the base line respectively. With the equipments of FieldSpectr Fr (made by ASD Co., US), we collected data from Baiya gold deposit, Yunnan, and applied the above method to discriminate altered rocks as an experiment. The results show satisfactory performance of the method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11371109)
文摘Let G be a graph with vertex set V（G） and edge set E（G）. A labeling f ： V（G） →Z2 induces an edge labeling f＊： E（G） → Z2 defined by f＊（xy） = f（x） ＋ f（y）, for each edge xy ∈ E（G）. For i ∈ Z2, let vf（i） = ｜{v ∈ V（G） ： f（v） = i}｜ and ef（i） = ｜{e ∈ E（G） ： f＊（e） =i}｜. A labeling f of a graph G is said to be friendly if ｜vf（0）- vf（1）｜ ≤ 1. The friendly index set of the graph G, denoted FI（G）, is defined as {｜ef（0）- ef（1）｜： the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS（n, m）.
文摘A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.
基金Supported by FRG/07-08/II-08 Hong Kong Baptist University
文摘Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.
基金the National Natural Science Foundation of China （No. 10671005） the Natural Science Foundation of Hebei Province （No. A2007000230）.
文摘In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;d] to exist.
基金This work was supported partly by the National Natural Science Foundation of China(Grant Nos.11801149,11801148)S.Wu was also partially supported by the Doctoral Fund of Henan Polytechnic University(B2018-55).
文摘Let G be a connected simple graph with vertex set V(G)and edge set E(G).A binary vertex labeling f:V(G)→Z2,is said to be friendly if the number of vertices with different labels differs by at most one.Each vertex friendly labeling/induces an edge labeling f*E(G)→Z2,defined by f*(xy)=f(x)+f(y)for each xy∈E(G).Let er(i)=\{e∈E(G):f*(e)=i}|.The full friendly index set of G,denoted by FFI(G),is the set{ef*(1)-ep(0):f is friendly}.In this paper,we determine the full friendly index set of a family of cycle union graphs which are edge subdivisions of P2×Pn.
文摘In this paper we will first give the characterization of the p^-low p^-degree,and prove that a p.r.e. degree(?)contains a p^-speedable set A if and only if(?)′>P(?)′.Then we classify the index sets of Low[n]~p and High[n]~p and prove that Low [n]~p is Σ~P[n+3]-complete and High [n]~p is Σ~P [n+4]-complete.
基金the Opening Project of the State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System(No.CEMEE2014K0301A)
文摘Radar anti-jamming performance evaluation is a necessary link in the process of radar development,introduction and equipment. The applications of generalized rough set theory are proposed and discussed in this paper to address the problems of big data, incomplete data and redundant data in the construction of evaluation index system. Firstly, a mass of real-valued data is converted to some interval-valued data to avoid an unacceptable number of equivalence classes and classification rules, and the interval similarity relation is employed to make classifications of this interval-valued data. Meanwhile, incomplete data can be solved by a new definition of the connection degree tolerance relation for both interval-valued data and single-valued data, which makes a better description of rough set than the traditional limited tolerance relation. Then, E-condition entropy-based heuristic algorithm is applied to making attribute reduction to optimize the evaluation index system, and final decision rules can be extracted for system evaluation. Finally, the feasibility and advantage of the proposed methods are testified by a real example of radar anti-jamming performance evaluation.
文摘背景消化性溃疡(PUD)是消化系统常见疾病,中医药治疗作为PUD的有效治疗措施,但目前针对中医药治疗PUD的随机对照试验(RCT)中,方法学质量、结局指标的选择等存在较大局限性,给疗效评价、资料整合分析等带来一定挑战。目的本文系统梳理近15年中医药干预PUD的RCT结局指标应用状况与试验设计要点,旨在为构建中医药治疗PUD核心指标集及优化临床试验设计提供参考依据。方法计算机检索中文数据库:中国知网、万方数据知识服务平台、维普网、中国生物医学文献服务系统,以及国际权威数据库:PubMed、Embase、Cochrane Library、Web of Science中关于中医药治疗PUD的RCT文献;检索时限为2010—2024年。对纳入文献进行Cochrane偏倚风险评估,并统计、归纳、分析相关结局指标。结果共纳入323篇RCT文献,34933例患者,单项研究样本量最大为498例,最小为40例,平均样本量为108例;171篇报告中医证型,其中使用频次最高为脾胃虚寒(31篇,18.13%);47篇采用纯中医治疗,276篇采用中西医结合治疗;治疗疗程多为4周(119次,36.84%);结局指标按照功能属性划分为6类,共报道了170种结局指标,总频次为1962次,其中使用频次较高的结局指标是临床总有效率(233次,11.88%)、幽门螺杆菌根除率(165次,8.41%)、不良反应(155次,7.90%);纳入文献偏倚风险评估多数为不明确。结论中医药治疗PUD的RCT尚存在中医辨证分型与疾病分期欠规范、方法学设计(盲法、分配隐藏)待完善、主次结局指标区分不明确、临床疗效标准未统一、结局指标测量时间差距大、中医证候/症状积分评分标准多元化、伦理注册待重视、安全性指标报告不规范等问题。建议积极开展中医药治疗PUD的核心指标集研究,优化完善方法学质量,为中医药治疗PUD的临床实践提供科学性、可靠性、实用性证据。
文摘为提高可消除项集的挖掘效率,在WPPC-Tree基础上提出优化后开始-结束序列树(start-finish-order tree,SFOTree),定义开始-结束序列集合(start-finish-order-set,SFO-Set)和开始-结束序列集合差(difference of start-finish-orderset,dSFO-Set),建立项集的收益索引,提出一种基于dSFO-Set的可消除项集挖掘算法。利用dSFO-Set性质和收益索引,提高项集收益的计算效率,减少可消除项集的挖掘代价。分别在稠密数据集和稀疏模拟数据集上与传统算法进行测试比较,实验结果表明,该算法具有更好的挖掘效率。
基金Project supported by the National Natural Science Foundation of China (Grant No.10672146)the Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.
基金supported by the UGC, SERO, Hyderabad under FDP during XI plan periodthe UGC, New Delhi for financial assistance under major research project Grant No. F-34-105/2008
文摘Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features may be redundant, and others may be irrelevant and noisy. The conventional supervised FS methods evaluate various feature subsets using an evaluation function or metric to select only those features which are related to the decision classes of the data under consideration. However, for many data mining applications, decision class labels are often unknown or incomplete, thus indicating the significance of unsupervised feature selection. However, in unsupervised learning, decision class labels are not provided. In this paper, we propose a new unsupervised quick reduct （QR） algorithm using rough set theory. The quality of the reduced data is measured by the classification performance and it is evaluated using WEKA classifier tool. The method is compared with existing supervised methods and the result demonstrates the efficiency of the proposed algorithm.
基金supported in part by Natural Science Foundation of Education Department of Sichuan Province under Grant No.12ZA178Key Technology Support Program of Sichuan Province under Grant No.2015GZ0102+1 种基金Science and Technology Project of Chongqing Municipal Education Commission under Grant No.KJ1400407Chongqing Science and Technology Commission Project under Grant No.cstc2014jcyj A10051
文摘The preference analysis is a class of important issues in multi-criteria ordinal decision making.The rough set is an effective approach to handle preference analysis.In order to solve the multi-criteria preference analysis problems,this paper improves the preference relation rough set model and expands it to multi-granulation cases.Cost is also an important issue in the field of decision analysis.Taking the cost into consideration,we also expand the model to the cost sensitive multi-granulation preference relation rough set.Some theorems are represented,and the granule structure selection based on approximation quality is investigated.The experimental results show that the multi-granulation preference rough set approach with the consideration of cost has a better performance in granule structure selection than that without cost consideration.
文摘The comprehensive evaluation method of enterprise core competitiveness is proposed by combining rough sets and gray correlation theories. Firstly,the initial index is screened through rough set attribute reduction algorithm,and the evaluation weight of each index is obtained through the rough set theory. Then,based on the gray correlation theory, an evaluation model is built for empirical analysis. The 30 financial institutions on the Yangtze River Delta are examined from the theoretical and empirical perspective.The result demonstrates not only the feasibility of rough set attribute reduction algorithm in the core competitiveness index system of the financial institution,but also the accuracy of the combination of these two methods in the comprehensive evaluation of corporate core competitiveness.
基金ThisresearchisjointlysupportedbytheNationalNaturalScienceFoun dationofChina (No .4 0 2 72 0 2 2 )andtheKeyBrainstormProjectoftheMinistryofLandandResourcesofChina (No .2 0 0 1 0 30 5)
文摘Field data of outcrop spectrums provide important basis for modeling of hyper-spectral remote sensing aiming at mineral prospecting. We make an approach to the application of rough set theory in spectral discrimination of rocks. We build a decision table with an adequate number of samples (outcrops) of known rock type (the universe), of which the conditional attributes are discretized 'area spectrum absorption indexes' (ASAI) corresponding to wavelength intervals, and the decision attribute is rock type. We search to obtain the exhaustive set of reducts of the table, each of which will serve as a variable number of deduction rules. Suppose we have n (usually a very big number) rules in total and there are m types of rocks in our universe, for any unknown sample, we judge its rock type by each of those rules. An unknown sample may be recognized as a different type by different rules because it is outside our universe, and we accept the most frequent judgment result and ignore the other m-1 types of results. Our ASAI is an improvement upon the traditional spectrum absorption index (SAI), better applicable to field spectrums: given a spectrum curve and a wavelength interval, we take the average reflectance within the interval as a base line and let ASAI=a below/(a above+a below), where a below and a above stand for total areas, bounded by the curve, the base line and the borders of the intervalbelow and above the base line respectively. With the equipments of FieldSpectr Fr (made by ASD Co., US), we collected data from Baiya gold deposit, Yunnan, and applied the above method to discriminate altered rocks as an experiment. The results show satisfactory performance of the method.
