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
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty ...We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.展开更多
The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function...The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.展开更多
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
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
This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary an...This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
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
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
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
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
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
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
In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets...The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.展开更多
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
Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressiv...Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
基金Sponsored by the National Natural Science Foundation of China (70771010)
文摘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.
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
文摘We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.
基金Project supported by the National Natural Science Foundation of China (No. 10371024) the Natural Science Foundation of Zhejiang Province (No.Y604003)
文摘The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.
基金supported by“1 Decembrie 1918”University of Alba Iulia,510009 Alba Iuliasupported in part by the HEC-NRPU project,under the grant No.14566.
文摘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.
基金fundings supported by Sichuan Science and Technology Program(2025YFHZ0065).
文摘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.
文摘This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
文摘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.
基金This project was surpported by the Natural Science Foundation of Shandong Province of China (Y2004A94)
文摘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.
基金This project was supported by Natural Science Foundation of Shandong Province of China (Y2004A04), Natural ScienceFoundation of Fujian of China (Z051049) and Education Foundation of Fujian of China (JA04268),.
文摘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.
基金the support of the National Natural Science Foundation of China under Grant No.60673023,60433020,10501017,3040016the European Commission for TH/Asia Link/010 under Grant No.111084.
文摘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.
基金Project supported by the Natural Science Foundation of China(10371009) and Research Fund for the Doctoral Program Higher Education.
文摘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.
基金Supported by the NSF of China(10771220)Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002)
文摘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.
文摘In this paper, the uniqueness of meromorphic functions with common range sets and deficient values are studied. This result is related to a question of Gross.
文摘The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.
基金supported by the National Key Re-search and Development Program of China(2020YFA0714200)supported by the Excellent Dissertation Cultivation Funds of Wuhan University of Technology(2018-YS-077)。
文摘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.
基金Project(2011AA060407) supported by the National High Technology Research and Development Program of China
文摘Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
