关于指数分布无失效数据的Bayes分析的注记

本文对指数分布无失效数据，在修正似然函数的基础上，给出了Ｂａｙｅｓ分析的方法，并与［１］中结果进行了比较，同时修正了［２］中的错误．     

几类特殊测地块的构造(英)

本文给出了一种构造给定直径d和围长g的测地块的方法．它是文［1］中构造法的推广，解决了文［1］中待研究的几个问题．同时，对文［1］中的一个错误进行了修正．     

修正多重尺度法在求解圆薄板具有很大挠度问题时的应用

本利用修正的多重尺度法＾［１～２］重新研究固支圆薄板在均匀压力作用下，挠度很大时解的渐近性态。结果表明与钱伟长教授用首创的合成展形法求解该问题＾［３］的结果相一致，但较后更简捷。本结果还表明［４］中所指出［１～２］方法的局限性是非本质的，并改正［３］中一些计算错误。     

Boole算子Fuzzy逻辑中推理的形式结构

在Boole算子Fuzzy逻辑中引入公式的恒真水平和恒假水平的概念,讨论了不确定性推理的形式结构,并推广了开放逻辑中的认识进程理论,给出了一种描述人类在具有不确定性、不一致性和不完全性知识下推理过程的方法。这种方法能够刻划具有不确定性知识的增长和修正以及认识的进化,反映了人类在推理过程中不断修正错误和进行信念的积累,从而得到有用结论的动态特征.     

修正单纯形法的计算量的注记

对文献［１］、［２］指出的修正单纯形法的计算量提出了异议,并给出了修正单纯形法应有的计算量。     

也谈费马─斯坦勒尔问题

也谈费马─斯坦勒尔问题刘凯年（重庆师范学院数学系６３００４７）文献［１］（见本刊１９９４年第３期）、［２］、［３］用不同方法解决了费马一斯坦勒尔问题．但［３］为实验解，未给出严格的数学证明，［１］、［２］的方法又比较繁难，且［１］的方法很难为中学生所...     

关于“集值算子的表示”一文的注记

本文通过一个反例说明［１］中一个主要定理是错误的，并给出其修正结果．     

修正的完全近似法的改进形式及其应用

本文对文［１］、［２］提出的修正的完全近似法作了改进：将自变量变换中的待定非线性泛函用特定非线性函数来代替，使运算简化；给出一种新的变换形式，解决了修正的完全近似法往往导出现长期项的问题。     

修正的高阶Hermite—Fejer插值的加权L^p逼近

本文给出了基于Ｃｈｅｂｙｓｈｅｖ结点的高阶Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值多项式的两种修正形式，并证明了这两种修正对ｆ∈Ｌｗ＾ｐ均可给出逼近阶ｗ（ｆ，１／ｎ）ｐ．同时文中也给出了基于Ｃｈｅｂｙｓｈｅｖ结点的Ｈｅｒ－ｍｉｔｅ－Ｆｅｊｅｒ及Ｈｅｒｍｉｔｅ插值多项式对Ｃ［－１，１］及Ｃ＾ｒ［－１，１］类函数的逼近阶。     

关于一个次线性逼近定理的新证法

Ｄｅｍｙａｎｏｖ和Ｒｕｂｉｎｏｖ在［１］中给出了一个次线性逼近定理．本文对该定理的证明进行了修正．     

Reply to the note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”

In a very recent note by Gao and Ni [B. Gao, M.F. Ni, A note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”, European Journal of Operational Research, in press, doi:10.1016/j.ejor.2007.10.0381], they argued that Yen’s combination rule [J. Yen, Generalizing the Dempster–Shafer theory to fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics 20 (1990) 559–570], which normalizes the combination of multiple pieces of evidence at the end of the combination process, was incorrect. If this were the case, the nonlinear programming models we proposed in [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35–66] would also be incorrect. In this reply to Gao and Ni, we re-examine their numerical illustrations and reconsider their analysis of Yen’s combination rule. We conclude that Yen’s combination rule is correct and our nonlinear programming models are valid.     

区间值不确定推理真值传播的计算方法

通过用方差定义左右修正量,将点值不确定推理真值传播计算方法推广到区间值情形,提出了一种区间值不确定推理真值传播计算方法.本文所提出的方法表达式简单,易于理解与计算.     

Combining sources of evidence with reliability and importance for decision making

The combination of sources of evidence with reliability has been widely studied within the framework of Dempster-Shafer theory (DST), which has been employed as a major method for integrating multiple sources of evidence with uncertainty. By the fact that sources of evidence may also be different in importance, for example in multi-attribute decision making (MADM), we propose the importance discounting and combination method within the framework of DST to combine sources of evidence with importance, which is composed of an importance discounting operation and an extended Dempster’s rule of combination. Three evidence combination axioms are proposed and explored to uncover the differences between reliability and importance in evidence reasoning. Furthermore, a general scheme is proposed for combination of sources of evidence with both reliability and importance. An example of car performance evaluation is studied to show the efficiency of the new general scheme.     

反对称自变量线性各向同性张量函数表示定理

本文给出了反对称自变量线性各向同性张量函数表示定理的两个证明:一个证明是新的;另一个基本上沿用[1]的思路,但较简短,且纠正了[1]的一个错误.     

基于云模型和证据推理的生态环境安全评价

文章提出了一种生态环境安全综合评价模型。首先构建生态环境安全评价指标体系并划分等级区间, 通过云模型将各指标实际值转化为生态环境安全等级的关联度; 其次结合证据推理与熵权法动静态组合确定指标权重; 然后利用证据推理计算出各指标基本可信度分配函数, 再采用证据融合算法合成出生态环境安全综合评估概率分布; 最后根据“最大关联度准则”得出评价结果。以湖南省为例开展实例研究, 研究结果与模糊综合评价法评估等级结果一致, 验证了所提出方法具有合理性、可行性和有效性。     

串联系统多参数广义不确定度传递模式与多反馈控制

将多参数广义不确定度的概念引入串联系统参数不确定度的传递问题中,建立了串联系统多参数广义不确定度传递模型,该模型不仅揭示了参数不确定度在传递过程中的变化情况,传递细节表明传递矩阵元素对最后的传递结果有重要影响.文中阐述了传递矩阵的特征以及各个子系统在串联系统中的主次作用.针对串联系统建立了多参数广义不确定度多反馈控制模型,提出了针对单个系统、两个子系统、多个子系统多个层次的反馈控制模型.模型的提出从理论上说明了当对子系统传递矩阵进行修正时,输出参数不确定度的变化及其上界的面积范数,为工程实际提供了一个良好的理论模型支撑.     

A modified Adomian's decomposition method

A modification of Adomian's method [1–4], based on the use of Padé approximants (5], is proposed. Examples are considered: a non-linear differential equation, a rectangular plate under transverse pressure, and a combination of transverse pressure and longitudinal compression.     

Unsteady propagation of longitudinal shear cracks

In all problems of unsteady crack propagation which have been solved to date [1 to 3], it has been assumed that the crack propagates at a constant speed. This assumption was not prompted by physical considerations of the problem, but by the methods of solution, therefore, the applicability of the results is limited. It would be more realistic to consider the speed of crack propagation as a function of time based on explicit physical hypotheses. Unfortunately, the general case of the resultant problem cannot be solved by existing methods. However, the problem of longitudinal shear cracks i.e. the plane problem in which the displacement is parallel to the crack boundary, may be solved for an arbitrary given variation in crack propagation speed, utilizing the method developed in connection with the theory of supersonic flows [4 and 5].

Note that equilibrium problems of longitudinal shear cracks have been studied in [6 and 7].     

The reliability of reasoning with unreliable arguments

Shafer's theory of evidence has found much interest as a means to represent and manage uncertainty in reasoning. It is shown that an important part of this theory can be recast as a theory of reasoning with unreliable arguments. This places the problem within the framework of the reliability theory of binary, monotone systems. Methods from this well developed theory can thus be used in the context of reasoning under uncertainty. This opens new computational perspectives for combining evidence. In particular, it allows for a backward chaining approach in judging hypotheses in the light of unreliable information. As a consequence, mechanisms to explain the judgments of hypotheses can be designed. The approach will be illustrated especially by the problem of reasoning in inference networks with uncertain rules and uncertain facts.     

Modeling attitudes towards uncertainty and risk through the use of choquet integral

The aim of this paper is to present in a unified framework a survey of some results related to Choquet Expected Utility (CEU) models, a promising class of models introduced separately by Quiggin [35], Yaari [48] and Schmeidler [40, 41] which allow to separate attitudes towards uncertainty (or risk) from attitudes towards wealth, while respecting the first order stochastic dominance axiom.