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Maximization of monotone non-k-submodular set function with noise under matroid constraints 认领 引用
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作者 Jiang Yanjun Wang Yijing +1 位作者 Yang Ruiqi Li Ali 《High Technology Letters》 EI CAS 2026年第1期73-83,共11页
Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular s... Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines. 展开更多
关键词 k-submodular set function greedy matroid constraints approximation algorithm
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Reliability Topology Optimization Based on Kriging-Assisted Level Set Function and Novel Dynamic Hybrid Particle Swarm Optimization Algorithm 认领 引用 被引量：1
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作者 Hang Zhou Xiaojun Ding +1 位作者 Song Chen Qijun Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第8期1907-1933,共27页
Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service lif... Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe. 展开更多
关键词 Reliability topology optimization kriging model level set function dynamic hybrid particle swarm optimization engineering structure
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Some properties of monotone set functions defined by Choquet integral 认领 引用 被引量：4
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作者 欧阳耀 李军 《Journal of Southeast University(English Edition)》 EI CAS 2003年第4期423-426,共4页
In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-ad... In this paper, some properties of the monotone set function defined by theChoquet integral are discussed. It is shown that several important structural characteristics of theoriginal set function, such as weak null-additivity, strong order continuity, property (s) andpseudomelric generating property, etc., are preserved by the new set function. It is also shown thatC-integrability assumption is inevitable for the preservations of strong order continuous andpseudometric generating property. 展开更多
关键词 non-additive measure monotone set function choquet integral
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A New Variational Model with Dual Level Set Functions for Selective Segmentation 认领 引用 被引量：3
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作者 Lavdie Rada Ke Chen 《Communications in Computational Physics》 SCIE 2012年第6期261-283,共23页
In this paper we present a selective segmentation model using a dual level set variational formulation.Our variational model aims to segment all objects with one level set function(global)and the selected object,which... In this paper we present a selective segmentation model using a dual level set variational formulation.Our variational model aims to segment all objects with one level set function(global)and the selected object,which is the closest to the geometric constraints(markers),with another level set(local).It is a combination of edge detection,markers distance function and active contour without edges.Experimental results show that our model is more robust than previous work. 展开更多
关键词 Image selective segmentation level set function Euler-Lagrange equation 2D image segmentation re-initialization
Set Function Optimization 认领 引用 被引量：1
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作者 Wei-Li Wu Zhao Zhang Ding-Zhu Du 《Journal of the Operations Research Society of China》 EI CSCD 2019年第2期183-193,共11页
This article is an introduction to recent development of optimization theory on set functions,the nonsubmodular optimization,which contains two interesting results,DS(difference of submodular)functions decomposition a... This article is an introduction to recent development of optimization theory on set functions,the nonsubmodular optimization,which contains two interesting results,DS(difference of submodular)functions decomposition and sandwich theorem,together with iterated sandwich method and data-dependent approximation.Some potential research problems will be mentioned. 展开更多
关键词 Set function Optimization DS decomposition・Sandwich theorem Iterated sandwich method
Function S-rough sets and mining-discovery of rough law in systems 认领 引用 被引量：26
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作者 Shi Kaiquan Xia Jiarong 《Journal of Systems Engineering and Electronics》 2006年第4期919-926,共8页
Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives... Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research. 展开更多
关键词 function S-rough sets structure of function S-rough sets relationship theorem rough law mining-discovery,applications.
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ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN 认领 引用 被引量：5
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作者 陈省江 林伟川 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期194-206,共13页
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu... In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary. 展开更多
关键词 Shared-set uniqueness meromorphic function angular domain infinite order
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Function S-rough sets and two law forecast 认领 引用 被引量：1
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作者 Fu Haiyan Shi Kaiquan 《Journal of Systems Engineering and Electronics》 SCIE EI 2009年第2期332-338,共7页
Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough ... Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province. 展开更多
关键词 function S-rough sets two law forecast dynamic economic system
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Function S-rough Sets and Their Law Characteristic 认领 引用 被引量：2
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作者 李东亚 史开泉 《Chinese Quarterly Journal of Mathematics》 北大核心 2007年第2期225-231,共7页
Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-roug... Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory. 展开更多
关键词 function one direction S-rough sets law the theorem of law-chain-attribute the theorem of law-belt
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COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE 认领 引用 被引量：2
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作者 房艮孙 叶培新 《Acta Mathematica Scientia》 SCIE 2005年第3期439-448,共10页
The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stoc... The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting. 展开更多
关键词 worst (deterministic) case stochastic case average case setting bounded linear functional error estimate
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Monotone Set-Valued Function Defined by Set-Valued Choquet Integral 认领 引用
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作者 孙红霞 张强 《Journal of Beijing Institute of Technology》 EI CAS 2010年第2期241-245,共5页
Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structu... Structural characteristics and absolute continuities of monotone set-valued function defined by set- valued Choquet integral are discussed. Similar to the single-valued monotone set function, several important structural characteristics of set-valued function are defined and have been proven the same as those in the original set functions, such as null-additivity, weakly null-additivity, order continuity, strong order continuity and property（S）. A counterexample shows that order continuity and strong order continuity of the original set functions are no longer kept in a monotone set-valued function when Choquet integrably bounded assumption is abandoned. Four kinds of absolute continuities are defined for set-valued function, and all been proven valid with respect to the original set functions. 展开更多
关键词 monotone set-valued function set-valued Choquet integral Choquet integral
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LEVEL SET METHODS BASED ON DISTANCE FUNCTION 认领 引用
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作者 王德军 唐云 +1 位作者 于洪川 唐泽圣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第8期950-960,共11页
Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is t... Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted. 展开更多
关键词 level set methods distance function existence and uniqueness of the solution
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Function S-Rough sets and its applications 认领 引用 被引量：25
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作者 Cui Yuquan Shi Kaiquan 《Journal of Systems Engineering and Electronics》 2006年第2期331-338,共8页
Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one ... Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system. 展开更多
关键词 function S-rough sets structure of function S-rough sets relationship theorem rough law mining-discovery applications.
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A Note on Normal Families of Meromorphic Functions and Sharing Set 认领 引用 被引量：1
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作者 XIAO Bing WU Qi-feng YUAN Wen-jun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期360-365,共6页
In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplic... In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D. 展开更多
关键词 entire function normal family meromorphic function share value set
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Rough Integrals Generated by Function Rough Sets 认领 引用 被引量：1
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作者 YU Xiu-qing XU Feng-sheng 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期296-299,共4页
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integ... The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic. 展开更多
关键词 function rough sets the lower approximation integral the upper approximation integral rough integrals
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Normal Families of Meromorphic Functions and Shared Set 认领 引用
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作者 TIAN Hong-gent CHEN Weit YUAN Wen-jun 《Chinese Quarterly Journal of Mathematics》 2015年第2期159-165,共7页
In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f h... In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m > 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results 展开更多
关键词 meromorphic function shared set normal family
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Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks 认领 引用
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作者 Levente Simon Anna Soós 《Applied Mathematics》 2016年第4期365-374,共10页
We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph model... We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks. 展开更多
关键词 Cantor Set Fixed Set Iterated Function Systems Iterated Multifunction Systems Self-Similar Graphs
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Undersea Buried Pipeline Reconstruction Based on the Level Set and Inverse Multiquadric Regularization Method 认领 引用 被引量：1
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作者 SHANG Wenjing XUE Wei +2 位作者 XU Yidong MAKAROV Sergey B LI Yingsong 《Journal of Ocean University of China》 SCIE CAS CSCD 2022年第1期101-112,共12页
The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance... The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless manner.However,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem.In this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried pipelines.In the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known conductivity.The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image.To obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from 0.We also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp edges.The simulation results and analysis show that the proposed method performs better than classical inversion methods. 展开更多
关键词 inverse problems level set function inverse multiquadric regularization method buried pipeline
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基于图拓扑结构和贪心算法的锚点选取优化 认领 引用
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作者 戴邵武 顾昊伦 《华南理工大学学报（自然科学版）》 EI CAS CSCD 北大核心 2026年第4期84-100,共17页
针对基于数据分发服务的分散式组网导航系统(DDS-DNNS)的锚点选取问题,构建了节点位置图以及节点位置估计模型,并将锚点选取问题表述为固定基数约束下最大化Fisher信息矩阵的D-最优度量问题,以此为基础,设计了基于图拓扑结构的DDS-DNNS... 针对基于数据分发服务的分散式组网导航系统(DDS-DNNS)的锚点选取问题,构建了节点位置图以及节点位置估计模型,并将锚点选取问题表述为固定基数约束下最大化Fisher信息矩阵的D-最优度量问题,以此为基础,设计了基于图拓扑结构的DDS-DNNS锚点选取优化算法。该算法利用图拓扑结构与Fisher信息矩阵D-最优度量之间的联系,将最大化Fisher信息矩阵的D-最优度量近似转化为最大化降维加权Laplacian矩阵的对数行列式值,并基于集合函数相关性质以及Cauchy交错定理证明了近似优化模型是一个非正则、非单调、非负的子模最大化问题,由此设计了包含基于近似最小度排序的稀疏Cholesky分解、惰性评估、矩阵维度保持及置换向量复用、Cholesky分解结果复用的改进贪心算法,用以求解近似优化模型,同时证明了该算法能提供近似优化性能保证,并具有远小于经典随机贪心算法的计算复杂度。最后,通过算例仿真比较了不同算法下位置估计效果、解算时间与锚点数量的关系,得到了固定基数约束的选取准则,验证了改进贪心算法在不同锚点数量下均能保证较高的估计精度,并有效降低计算复杂度。 展开更多
关键词 锚点选取 图拓扑 D-最优度量 集合函数 子模性 改进贪心算法
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Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction 认领 引用
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作者 Ran Yin Minge Chen +2 位作者 Yu Liu Yafei Zhao Jianwei Li 《Journal of Applied Mathematics and Physics》 2024年第7期2347-2366,共20页
As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and furth... As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value. 展开更多
关键词 Pseudo-Semi-Overlap Functions Fuzzy Rough Set Fuzzy Mathematical Morphology Image Edge Extraction
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