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在本文中,针对蕴涵算子$R_0$,我们给出了当$A\rightarrow B$与$A^*(B^*)$给定时,求使三I表达式$(A\rightarrow B)\rightarrow(A^*\rightarrow B^*)$取最小值的全体$B^*(A^*)$之集的上确界(下确界)算法.并将上确界算法推广到多维多重的模糊推理中.从三I表达式取最值时求最优的$B^*(A^*)$的角度来看,本文是三I算法思想的延伸和完善. 相似文献
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The problem of the influence of fuzzy implication operators and connective also on the accuracy of a fuzzy model of a d.c. series motor is considered. Several typical fuzzy implication operators are used to construct the fuzzy model of a d.c. series motor. A root-mean-square error is adopted as the criterion of the model's adequacy to the real system. The best typical fuzzy relations are selected. 相似文献
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基于直觉模糊熵权和CC-OWA算子的雷达目标识别模型 总被引:1,自引:0,他引:1
为更完整的描述和表达雷达目标类型识别中的目标特征和目标类型之间的关系复杂性和知识缺乏性,通过直觉模糊关系描述,进而将目标识别特征信息转化为直觉模糊集信息.分析了基于直觉模糊集理论的雷达目标类型识别知识建模,揭示了直觉模糊信息的价值可以通过直觉模糊熵刻画,进而提出应用直觉模糊集的熵构造特征直觉模糊信息的权重(直觉模糊熵权),充分利用了目标类型识别知识中隐含的权重信息,并结合CC-OWA算子建立雷达目标类型识别模型与识别步骤,利用一个雷达目标识别实例说明了模型的有效性. 相似文献
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设H1和H2是两个Hilbert空间,B(H1,H2)表示从H1到H2的所有有界线性算子的集合,T和S分别是H1和H2的两个闭子空间.如果存在线性算子X∈B(H2,H1)满足XAX=X,R(X)=T,N(X)=S,则称X为线性算子A的具有指定像空间T和零空间S的外逆,记为AT,S(2).该文进一步研究了线性算子广义逆AT,S(2)存在的若干等价条件及其性质,建立了算子广义逆AT,S(2)的表示形式. 相似文献
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模糊推理三I算法的逻辑基础 总被引:14,自引:9,他引:5
在模糊推理理论中,近期问世的三I推理方法以逻辑蕴涵运算取代传统的合成运算,从根本上改进了传统的合成推理规则(即CRI方法)。本文基于模糊命题逻辑的形式演绎系统L^*和模糊谓词逻辑的一阶系统K^*,构建了一个完备的多型变元一阶系统Kms^*,并且将三I算法完全纳入了模糊逻辑的框架之中,从而为模糊推理奠定了严格的逻辑基础。 相似文献
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Jue Wang San-Yang Liu Jie Zhang Shou-Yang Wang 《Fuzzy Optimization and Decision Making》2006,5(1):5-20
The family of Ordered Weighted Averaging (OWA) operators, as introduced by Yager, appears to be very useful in multi-criteria
decision-making (MCDM). In this paper, we extend a family of parameterized OWA operators to fuzzy MCDM based on vague set
theory, where the characteristics of the alternatives are presented by vague sets. These families are specified by a few parameters
to aggregate vague values instead of the intersection and union operators proposed by Chen. The proposed method provides a
“soft” and expansive way to help the decision maker to make his decisions. Examples are shown to illustrate the procedure
of the proposed method at the end of this paper. 相似文献
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We propose a convergence analysis of the generalized forward-backward splitting iterative procedure for the minimization of the sum of two functions in Banach spaces. The generalized forward-backward splitting method is applied to the minimization of functionals of the Tikhonov type with semi-norm regularization. We also investigate the perturbed forward-backward splitting method and prove its stability. 相似文献
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The influence of fuzzy implication operators and the connective Also on the accuracy of a fuzzy model of a d.c. series motor is considered. Some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d.c. series motor. A root-mean-square error is used as the criterion of the fuzzy model's adequacy to the real system. A number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model's applicability if estimated from the point of view of computing techniques. The best types of fuzzy relations, representing fuzzy models of a real system, are chosen in order to secure the least root-mean-square error with minimal number of mathematical operations necessary for computer implementation. 相似文献
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在应用多属性决策理论求解应急响应预案评估问题时,问题结构的复杂性往往使决策者评价信息存在高度不确定性且属性相对重要性仅能以优先级关系来表征。为此,本文首先提出了双边犹豫模糊非均衡语言集这种新型信息形式以使决策者能够灵活有效的表征复杂评价信息,并定义了运算法则、熵和距离测度;其次,基于熵测度开发了双边犹豫模糊非均衡语言优先加权集成算子,并构建了能够考虑属性优先关系的多属性决策方法;进一步针对属性相对重要性不能由定性分析获得的情况,设计了客观权重确定方法,并构建了另一种更具实际灵活性的VIKOR决策方法;最后,实例研究表明了方法的有效性与优势。 相似文献
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《International Journal of Approximate Reasoning》2014,55(6):1369-1382
Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning. 相似文献
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本文将粗糙集理论与模糊集理论结合起来,给出一种图书馆最优选书算法.该算法首先从已知数据的初始信息系统出发,计算各选书方案之间的相似度,从而构造相似矩阵,然后根据相似矩阵的传递闭包对各方案进行聚类,并根据粗糙集理论求各属性重要性,最后利用加权综合的思想及最小距离方法选择最优买书方案. 相似文献
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唐建国 《数学物理学报(A辑)》2003,23(3):265-275
该文研究了基于Chebyshev和Jacobi多项式的解不适定算子方程的隐式迭代法.建立了隐式迭代法和由Hanke提出的显式迭代法之间的关系. 给出了与Chebyshev第一和第二多项式相关的迭代格式的残差有理式的一个重要引理. 对精确和扰动的数据, 研究了方程的收敛性和收敛速率. 利用Morozov残差原则, 给出了一个可执行的强健的正则化算法.最后还给出了一些数值例子, 数值结果与理论分析基本一致. 相似文献
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不同直觉模糊数在信息集结过程中,其隶属度与非隶属度之间可能存在着相互影响.提出了直觉模糊数上的改进的乘法运算和幂运算,重新给出了直觉模糊加权几何平均算子和直觉模糊有序加权几何平均算子的表达式,并研究了他们的一些性质.最后通过实例说明了新的IFWGA集成算子在多属性决策中的应用是可行和有效的. 相似文献
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针对指标数据已知,而权重数据未知的群组赋权问题,给出了一种基于改进的区间数密度集结算子来进行指标群组赋权的决策方法。首先给出了区间数和区间数密度集结算子(IDM)的定义及性质,改进了以前区间数聚类的方法,应用直接法对一维区间数据组进行聚类,并定义了模糊统计量,以确定最为合理的一种聚类方式。然后基于改进的区间数密度集结算子这种数学模型,来解决指标值数据已知,而权重未知的群组赋权问题。最后举例说明该方法的可行性和实用性。 相似文献