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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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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 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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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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Function S-rough sets and law identification 认领 引用 被引量：77
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作者 SHI KaiQuan YAO BingXue 《Science in China(Series F)》 2008年第5期499-510,共12页
By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets （singular rough ... By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets （singular rough sets）. S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class （law equivalence class） that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets （function singular rough sets）. Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification. 展开更多
关键词 function S-rough sets system law law identification identification criterion identification theorem
Function S-rough sets and security-authentication of hiding law 认领 引用 被引量：70
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作者 SHI KaiQuan ZHAO JianLi 《Science in China(Series F)》 2008年第7期924-935,共12页
Function S-rbugh sets are defined by R-function equivalence class,which have dynamic characteristic.Function S-rough sets have dynamic characteristic,law characteristic and law-hiding characteristic.Function S-rough s... Function S-rbugh sets are defined by R-function equivalence class,which have dynamic characteristic.Function S-rough sets have dynamic characteristic,law characteristic and law-hiding characteristic.Function S-rough sets can generate f-hiding law and f-hiding law.By engrafting,crossing,and penetrating between the information security theory and function S-rough sets,the security hiding and the authentication of f-hiding law and f-hiding law are given respectively in this paper.The fusion and share between function S-rough sets and information security theory is a new research direction of the application of information law in information system. 展开更多
关键词 function S-rough sets law-hiding elliptic curve the security-authentication of hiding law
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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A Method of Gene-Function Annotation Based on Variable Precision Rough Sets 认领 引用 被引量：5
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作者 Zhi-li Pei Xiao-hu Shi +4 位作者 Meng Niu Xu-ning Tang Li-sha Liu Ying Kong Yan-chun Liang 《Journal of Bionic Engineering》 SCIE EI 2007年第3期177-184,共8页
It is very important in the field of bioinformatics to apply computer to perform the function annotation for new sequenced bio-sequences. Based on GO database and BLAST program, a novel method for the function annotat... It is very important in the field of bioinformatics to apply computer to perform the function annotation for new sequenced bio-sequences. Based on GO database and BLAST program, a novel method for the function annotation of new biological sequences is presented by using the variable-precision rough set theory. The proposed method is applied to the real data in GO database to examine its effectiveness. Numerical results show that the proposed method has better precision, recall-rate and harmonic mean value compared with existing methods. 展开更多
关键词 gene function annotation variable precision rough set GO BLAST
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α-LIMIT SETS AND LYAPUNOV FUNCTION FOR MAPS WITH ONE TOPOLOGICAL ATTRACTOR 认领 引用 被引量：2
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作者 Yiming DING Yun SUN 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期813-824,共12页
We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map wi... We consider the topological behaviors of continuous maps with one topological attractor on compact metric space X.This kind of map is a generalization of maps such as topologically expansive Lorenz map,unimodal map without homtervals and so on.Under the finiteness and basin conditions,we provide a leveled A-R pair decomposition for such maps,and characterize α-limit set of each point.Based on weak Morse decomposition of X,we construct a bounded Lyapunov function V(x),which gives a clear description of orbit behavior of each point in X except a meager set. 展开更多
关键词 Attracting set leveled A-R pair decomposition α-limit set Lyapunov function
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S-rough sets and knowledge separation 认领 引用 被引量：105
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作者 Shi Kaiquan 《Journal of Systems Engineering and Electronics》 2005年第2期403-410,共8页
The conceptions of the knowledge screen generated by S-rough sets are given:f-screen and f--screen,and then puts forward f--filter theorem,f--filter theorem of knowledge.At last,the applications of knowledge ... The conceptions of the knowledge screen generated by S-rough sets are given:f-screen and f--screen,and then puts forward f--filter theorem,f--filter theorem of knowledge.At last,the applications of knowledge separation are given according to f--screen and f--screen. 展开更多
关键词 S-rough sets f-screen -screen f-filter theorem -filter theorem knowledge separation.
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Julia sets of semi-conjugated transcendental entire functions 认领 引用 被引量：1
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作者 王小灵 孙朗伟 +1 位作者 杨德贵 鲍远圣 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2008年第3期383-385,共3页
Suppose that f and g are two transcendental entire functions, and h is a non-constant periodic entire function. We denote the Julia set and Fatou set off by J（f） and F（f）, respectively, lffand g are semiconjugated... Suppose that f and g are two transcendental entire functions, and h is a non-constant periodic entire function. We denote the Julia set and Fatou set off by J（f） and F（f）, respectively, lffand g are semiconjugated, that is, h · f = g · h, in this paper, we will show that z ∈ J（f） if and only if h（z） ∈ J（g） （ similarly, z F（f） if and only ifh（z） ∈ F（g））, and this extends a result of Bergweiler. 展开更多
关键词 Fatou component Julia set transcendental entire functions
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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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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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Basis Sets Dependency in Constructing Spectroscopy-Accuracy Ab Initio Global Electric Dipole Moment Functions 认领 引用
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作者 Yu Zhai Hui Li 《Chinese Journal of Chemical Physics》 SCIE EI CAS CSCD 2022年第1期52-57,I0062,共6页
Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential ... Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do.In this letter,using Ar…He as an example,we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods.We especially focused on the basis set dependency in this scenario,i.e.,the convergence of DMF with the sizes of basis sets,basis set superposition error,and mid-bond functions.We also tested the explicitly correlated method,which converges with smaller basis sets than the conventional methods do.This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs. 展开更多
关键词 Dipole moment function Ab initio computation High-accuracy computation Basis set
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Innovative Aczel Alsina Group Overlap Functions for AI-Based Criminal Justice Policy Selection under Intuitionistic Fuzzy Set 认领 引用
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作者 Ikhtesham Ullah Muhammad Sajjad Ali Khan +3 位作者 Fawad Hussain Madad Khan Kamran Ioan-Lucian Popa 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第8期2123-2164,共42页
Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM te... Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved.To address this issue,we propose a novel framework that integrates group and overlap functions with Aczel-Alsina(AA)operational laws in the intuitionistic fuzzy set(IFS)environment.Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments,while the Group functions are used to combine different expert opinions into a single collective result.This study introduces four new aggregation operators:Group Overlap function-based intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Averaging(GOF-IFAAWA)operator,intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Geometric(GOF-IFAAWG),intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)OrderedWeighted Averaging(GOF-IFAAOWA),and intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Ordered Weighted Geometric(GOF-IFAAOWG),which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping,uncertain,and hesitant information.The properties of these operators are discussed in detail.Further,the effectiveness,validity,activeness,and ability to capture the uncertain information,the developed operators are applied to the AI-based Criminal Justice Policy Selection problem.At last,the comparison analysis between prior and proposed studies has been displayed,and then followed by the conclusion of the result. 展开更多
关键词 Fuzzy sets(FS) intuitionistic fuzzy set(IFS) group function(GF) overlap function(OF) aczel alsina(AA)operators multi-criteria decision making problem(MCDM)
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Meromorphic Functions That Share Three Sets 认领 引用
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作者 张庆彩 《Northeastern Mathematical Journal》 2007年第2期103-114,共12页
In this paper we study the problem of meromorphic functions sharing three sets and obtain some theorems which are the extension and complement of some known relative results given by Yi Hongxun and others.
关键词 meromorphic function shared value shared set
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S-rough sets and the discovery of F-hiding knowledge 认领 引用 被引量：3
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作者 Hao Xiumei Fu Haiyan Shi Kaiquan 《Journal of Systems Engineering and Electronics》 SCIE EI 2008年第6期1171-1177,共7页
Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding propert... Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding properties are the basic characteristics of S-rough sets. By using the S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree, and hiding dependence degree are given. Then, both the hiding theorem and the hiding dependence theorem of hiding knowledge are proposed. Finally, an application of hiding knowledge is discussed. 展开更多
关键词 one-direction S-rough sets f-hiding knowledge hiding degree hiding dependence degree hiding theorem hiding dependence theorem application
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Two-scale topology optimization of structural fundamental eigenfrequency using a data-driven microstructure model based on M-VCUT level set 认领 引用
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作者 Zibo Wang Minjie Shao Qi Xia 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第2期437-447,共11页
For the optimization of fundamental eigenfrequency in vibrating structures,it has been proven that multi-scale structures have advantages over single scale structures.This study introduces a two-scale topology optimiz... For the optimization of fundamental eigenfrequency in vibrating structures,it has been proven that multi-scale structures have advantages over single scale structures.This study introduces a two-scale topology optimization method using a data-driven microstructure model based on a multiple variable cutting(M-VCUT)level set approach.This method aims to maximize the fundamental eigenfrequency of two-scale structures.The method consists of two parts:offline database construction and online topology optimization.In the process of offline database construction,many microstructures are obtained by varying the value of geometric parameters according to the M-VCUT level set approach;then,a mapping relationship between the geometric parameters and the homogenized mechanical properties of microstructures is established by compactly supported radial basis function interpolation,which gives the data-driven microstructure model.In the process of online optimization,the homogenized mechanical properties corresponding to arbitrary design variables are obtained by using the data-driven microstructure model,whose computational costs are much less than those of the homogenization.Topology optimization is carried out with this data-driven model to enhance computational efficiency.In order to adapt the method of moving asymptotes(MMA),the eigenfrequency maximization problem is converted to its reciprocal minimization problem for sensitivity calculation.The method’s effectiveness is proved through several numerical examples. 展开更多
关键词 Two-scale structure Data-driven M-VCUT level set Eigenfrequency optimization Radial basis function MMA
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Approximate solutions and nonlinear scalarizations for set optimization with a co-radiant set 认领 引用
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作者 ZHANG Qi XU Yi-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2026年第2期367-385,共19页
In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization ... In normed linear spaces,by applying the Minkowski difference,the concepts of efficient solutions,weakly efficient solutions,proper efficient solutions and Henig efficient solutions are introduced for set optimization with respect to co-radiant sets,and the relationships among them is discussed.Optimality conditions for minimal solutions and strictly minimal solutions of scalar set optimization are established by using the generalized oriented distance functions,respectively.The relationship between the solutions of set optimization problem and the solutions of scalar problem is studied.Several examples are given to explain our result.Properties of Gerstewitz’s functions with respect to co-radiant sets are discussed,which are used to establish sufficient conditions for weakly efficient solutions of set optimization. 展开更多
关键词 set optimization nonlinear function approximate solution co-radiant set
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SOME RESULTS ON TOPICAL FUNCTIONS AND UPWARD SETS 认领 引用
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作者 H.Hosni M.R.Haddai H.Mazaheri 《Analysis in Theory and Applications》 2011年第4期301-308,共8页
The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets. We give characterizations of topical functions in terms of upward sets.
关键词 topical function upward set ordered Banach space
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