直觉模糊关系及其合成运算

系统研究了作为Zadeh模糊集理论重要扩展的Atanassov直觉模糊关系及其合成运算.在考察Atanassov直觉模糊集与Zadeh模糊集之间关系的基础上,首先引入直觉模糊集及范数的概念、定义和性质,对直觉模糊集之间的一般关系、逆关系、零关系、全关系、恒等关系及其合成运算等进行了定义,研究了它们进行关系运算的基本规则、特殊性质及相关定理,且给出了必要的证明过程.揭示了直觉模糊关系的自反性、对称性及传递性,证明了直觉模糊关系合成运算的结合律定理.把Atanassov算子对于直觉模糊关系性质的影响,即对于自反性、对称性、逆对称性、完全逆对称性及传递性等性质的影响,归纳为该算子的效用性质和等价性质两个定理.     

模糊聚类中的模糊等价矩阵

在模糊相似关系方程Ｘ２＝Ｘ的分解构造理论基础上,用泛函分析方法证明了与给定的模糊相似阵距离最近的最优模糊等价阵的存在性与局部唯一性;还证明了局部最优模糊等价阵与给定的相似阵之间的数值关系．另外还讨论了传递闭包与最优模糊等价阵之间的关系．最后给出了传递核的概念,并讨论了其基本性质.     

直觉模糊等价矩阵构造方法

对直觉模糊相似关系和等价矩阵构造问题进行了深入研究,提出一种利用求传递闭包来构造直觉模糊等价矩阵的方法,并从理论上给出了相关证明.首先,利用直觉模糊合成运算及其结合律,相关引理和数学归纳法证明了直觉模糊相似矩阵R的任意k次合成运算也是直觉模糊相似矩阵的定理.其次,综合运用直觉模糊最小传递矩阵的概念及相关引理,证明了n阶直觉模糊矩阵的传递闭包定理和n阶直觉模糊相似矩阵定理,推导出包含R的最小直觉模糊等价矩阵的推论.最后指出,可以从一个直觉模糊相似矩阵R出发,利用连续合成运算求传递闭包的方法来构造一个直觉模糊等价矩阵.     

基于结构元方法的模糊矩阵博弈求解

在博弈论中,要求模糊数的序不仅要有好的分辨能力,还要满足经济人理性的假说.为此,提出了元序概念,并证明该序为全序.利用结构元相关定理,证明了m×n阶模糊矩阵必存在一m×n阶实数矩阵与其对应,且二者有相同的纳什均衡解.进而,利用结构元方法简化了模糊博弈矩阵的求解.最后,通过一个实际例子,表明了该方法的有效性.     

粗糙近似算子的拓扑性质

通过闭包与内部算子研究模糊粗糙集的拓扑结构,证明了自反、传递关系下的近似空间中模糊集的上、下近似算子分别为一个模糊拓扑的闭包、内部算子,且相应的模糊拓扑满足(TC)条件;反之,满足(TC)条件的模糊拓扑的闭包与内部算子也恰为一自反、传递关系下的近似空间中的上、下近似算子.     

Fuzzy Syntactic Congruence and Rational Fuzzy Languages

1　 IntroductionSince E.T.Lee and L.A.Zadeh gave the conceptoffuzzy finite-state automaton in1 969[2 ] ,the theory has been developed by researchers[1 ,3,4] . In this paper the fuzzy syntacticcongruence—another characterization of rational fuzzy language is dicussed.In the following text,we suppose thatΣ is an alphabetwith 1 |Σ|<∞ ,andΣ* isa free monoid generated fromΣ with the operation of adjoin,and F(Σ) denotes the setofall fuzzy subsets ofΣ,P(Σ) denotes the power setofΣ ,and …     

基于T-S模型的约束鲁棒保性能飞行控制律设计

对一类具有范数有界参数不确定Takagi-Sugeno (T-S)模糊模型系统,采用状态反馈并行分配补偿结构,综合考虑变量约束和多个性能指标,研究了约束鲁棒最优保性能飞行控制律设计问题。改进输入、输出及状态约束线性矩阵不等式,提出了带约束模糊最优保性能控制定理。在一般抗干扰控制基础上引入不确定性矩阵,证明了模糊鲁棒最优抗干扰定理。综合上述结论,推导出带约束模糊最优保性能抗干扰定理。最后,建立了飞机不确定T-S模糊模型,分别设计了满足上述3个定理的飞行控制律,并进行了仿真与对比分析,结果验证了该设计方法的有效性。     

On the axioms of revealed preference in fuzzy consumer theory

The revealed preference is a central subject in classical consumer theory.Authors likeSamuelson,Arrow,Richter,Sen,Uzawa and others have proposed an axiomatic setting of revealedpreference theory.Consequently revealed preference axioms WARP and SARP and congruence axioms WCA andSCA have been considered.An important theorem of Sen establishes the equivalence between these axioms provided thefamily of budgets includes all non-empty finite sets of bundles.Fuzzy consumer theory(＝fuzzy choice functions)is a topic that appears in a lot of papers.Particularly,Banerjee studies in fuzzy context axioms of revealed preference and congruenceextending some results of Arrow and Sen.In this paper we modify the Banerjee definition of a fuzzy choice function(＝fuzzy consumer)and we study some fuzzy versions of the axioms of revealed preference and congruence.Banerjeefuzzifies only the range of a consumer;we use a fuzzification of both the domain and the range of aconsumer.The axioms WAFRP,SAFRP,WFCA,SFCA generalize to fu     

TRANSFORMATION THEOREMS AMONG CAYLEY-KLEIN GEOMETRIES

A theorem of transformation between two geometries is proved on the basis of Wu's method of mechanical theorem proving.By using this theoremfor Cayley-Klein geometries of dimension two,we prove that the nine Cayley-Klein geometries can be divided into three groups within which the geometries aremutually equivalent in the sense that certain geometry statements are correct inone geometry if and only if they are correct in the other geometries of the samegroup.This means that for each group we only need to choose a model geometryto study and the theorems of other geometries in the same group can be obtainedfrom the model geometry automatically.The three model geometries chosen forthe nine Cayley-Klein geometries are:Euclidean geometry,Riemann geometry,andGalilean geometry.     

基于模糊偏序关系的混合型多属性决策方法

针对权重已知且属性值为精确实数型、区间型和模糊型的混合型多属性决策问题,提出了一种基于模糊偏序关系的混合型多属性决策方法。该方法利用混合型评估值模型来描述多属性决策问题;在对属性值预处理后,通过构建混合型模糊偏序关系模型,将决策问题转化为评估关系模型;然后对偏序关系进行集结,得到全序关系,从而获取所有方案的优劣排序。算例验证了方法的有效性。计算过程表明,该方法计算简单,且避免了逼近理想解的排序方法(technique for order preference by similarity to ideal solution,TOPSIS)难以合理定义距离函数的局限性。     

基于LBS的移动定向优惠券策略

考虑市场上存在两个非对称竞争性厂商，强势品牌厂商比弱势品牌厂商拥有更多的忠诚消费者。研究了竞争性厂商为消费者发放基于LBS的移动定向优惠券的策略，探讨了单位定向成本对厂商的定向促销策略（包括移动优惠券的优惠力度、定向范围、推送对象等）、市场均衡和社会福利的影响。研究结果表明，单位定向成本大小会影响厂商是否发放定向优惠券；厂商发放基于LBS的定向优惠券不一定会导致囚徒困境；在一定条件下基于LBS的定向促销会增加消费者剩余和社会福利。     

LROTH''''S THEOREM IN DIFFERENTIAL FIELDS

In this paper, we present a constructive proof of Luroth's theorem in differential case. We also give a method to find the inversion maps for general differential rational parametric equations. As a consequence, we prove that a differential rational curve always has a set of proper parametric equations.     

模糊偏好下群决策结构的研究

研究了群决策问题的模糊偏好关系 ,在模糊理性条件下证明了一个不可能定理 ,提出了影响集的概念 ,讨论了对群决策产生影响的影响集的结构 ,并给出了一个实例.     

内P-集合与F-内嵌入信息发现-辨识

P-集合是由内P-集合X^F 与外P-集合X^F 构成的有序集合对,它具有动态特性。利用内P-集合X^F,给出F-内嵌入信息(x)^F、F-内嵌入系数IEC(x)^F 与F-内嵌入度IED(x)^F的概念,得到F-内嵌入信息存在性定理、依赖关系定理与可辨识性定理。在这些概念与结果的基础上,给出F-内嵌入信息在目标搜索中的应用。     

OPTIMAL VALUE FUNCTIONS IN MATHEMATICAL PROGRAMMING AND CONVERGENCE FOR GRADIENT PROJECTION METHOD

ＯＰＴＩＭＡＬＶＡＬＵＥＦＵＮＣＴＩＯＮＳＩＮＭＡＴＨＥＭＡＴＩＣＡＬＰＲＯＧＲＡＭＭＩＮＧＡＮＤＣＯＮＶＥＲＧＥＮＣＥＦＯＲＧＲＡＤＩＥＮＴＰＲＯＪＥＣＴＩＯＮＭＥＴＨＯＤ￥ＷＡＮＧＣｈａｎｇｙｕ；ＺＨＡＯＦｕａｎ（ＩｎＳｔｉｔｕｔｅｏｆＯＲ，Ｑｕ...     

THERE IS NO MATHEMATICAL VALIDITY FOR USING FUZZY NUMBER CRUNCHING IN THE ANALYTIC HIERARCHY PROCESS

1. Introduction In this brief note we show that although fuzzy thinking may be useful in some engineering practices where so called crisp numbers are obtained from counting or from using scales of measurement, it is highly controversial and not very useful to use it in decision making where the numbers assigned to judgments are already fuzzy and making them more fuzzy does not help produce more valid outcomes. Not only can this be shown with examples, but what makes our assertion more to the p…     

HEALTH CONSUMER DIVERSITY AND ITS IMPLICATIONS

1. Introduction The health care scene in the Western world is shifting rapidly. Health care consumers have abandoned their traditionally respectful attitudes and behaviours. In the past the roles of the health consumers and providers were quite clear. The patients consumed and the health care providers provided (Edgren 1998). Today theJOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING 35 picture is more complex. Many health care consumers no longer want to be passive receiv…     

再论C2R模型的最优解的存在性及灵敏度分析

在评价指标可取负值及较宽松的条件下论证了有关C^2R模型(D)及扩展的C^2R模型(D0)的最优解存在性定理．然后，在输出可取负值的情况下，给出了用(D0)来判断DEA有效的定理，并据此讨论了评价指标有相对误差时的灵敏度分析．     

基于能力降阶的军事信息系统毁伤评估模型

针对信息系统毁伤评估中评估目标难以界定的问题,提出了基于能力降阶的毁伤评估模型,将支撑作战任务的信息能力降阶为子任务能力级、信息服务级和服务组件级。分析了毁伤在上下级之间的逻辑传递关系、线性传递关系、指数衰减关系和门限判别关系,并基于解释结构模型,构建毁伤影响关系矩阵,用以分析同级之间的毁伤级联传播关系,定义模型的毁伤评估树结构和评估计算步骤。最后,以防空反导指挥信息系统为算例,分析验证了模型的有效性。     

不确定环境下的两层交互式有限理性决策方法

为解决不确定环境下决策成员具有有限理性行为特征的两层决策问题,基于概率权重具有稳定性和结果价值具有模糊性两项合理假设命题,从平衡上下两层满意度视角提出了用于确定最优结果价值和最优概率权重的两层决策模型及相关定理,同时给出了实现决策方案有限理性全排序的两层交互式决策方法.模拟验证结果表明,该方法不仅在理论上是科学有效的而且在实际应用上是可行的.