逻辑系统-↑W，W，Wk中的广义语义HS规则和广义语义MP规则

研究模糊命题演算的形式演绎系统L及在语义上相关的修正的Kleene逻辑系统-↑W，W，Wk，引入语义[α]-MP规则，语义[α^ ]-MP规则，语义[α]-HS规则，语义[α^ ]-HS规则等概念，并对这些规则的性质进行讨论，进一步加强该系统中的∑-(α-重言式)的相应结果，丰富该系统中∑-(α-重言式)的内容，为进一步研究该系统提供一个有益的工具。     

直觉主义类型论中π和Σ规则的研究

本文研究直觉主义类型论中π和Σ规则，对于类型（πｘ∈Ａ）Ｂ（ｘ），我们给出新的消去和相等规则使新规则的式样与其他类型的规则相同，然而不使用高阶交元和常元，我们证明新规则等价于旧规则，对于类型（Σｘ∈Ａ）Ｂ（ｘ），我们利用投影运算给出新规则，而且证明它们等价于旧规则。     

线性回归系数的修约规则

线性回归系数的修约规则黄映辉（西安交通大学管理学院）线性回归根据存有相互关系的变量ｙ，ｘｔ的观测值来确定回归系数ａ和ｂｉ，从而建立线性回归方程。因为观测值ｙ和ｘｉ通常为近似数，所以由ｙ和ｘｉ计算而得的回归系数ａ和ｂｉ也必为近似数，其修约误差可由ｙ，ｘ...     

退化问题中Bland规则的改进

Bland规则是退化问题中避免循环的一种方法，本给出了Bland规则的两种改进形式，并从理论上证明了规则Ⅲ为有限规则，另外，还对一个退化问题给出了相应于不同规则的解法。     

网站用户登录信息挖掘特征规则

本文首先研究了基本的面向属性归纳，提出了从网站用户登录信息中挖掘用户特征规则的思路。问题从解决多属性归纳着手，特点是首先建立概念树，然后用条件属性组合与约束的方法进行挖掘。实验表明，本文设计的模型能客观地描述客户行为，为从Web信息挖掘客户特征规则提出了一条有效的途径。     

模糊规则提取的两种方法性能分析

机器学习近年来得到越来越多的重视，模糊规则提取是其中的重要的一个方向。本文介绍了两种自动提取模糊规则的方法，分别是基于多层前向网络和基于遗传算法的模糊规则自动生成。并且，详细的分析了两种方法性能     

少数服从多数规则的特性

假定投票人的人数是奇数，E．S．Maskin引入传递性刻画了少数服从多数规则的特性．Campbell和Kelly试图将E．S．Maskin的理论推广到投票人的人数是任意整数的情形，用有限传递性来刻画少数服从多数规则的特性．我们发现存在这样的少数服从多数规则，它满足无关方案独立性条件并且认为任意两个不同的备选方案都是有差异的，但却不一定满足有限传递性．所以，用有限传递性来刻画少数服从多数规则的特性就有一定缺陷．本文对满足无关方案独立性的少数服从多数规则特性进行了重新刻画，并弱化了有关条件．     

组合逻辑中的一个新的(ξ)规则

作者提出一个新的规则（ξ０），在组合逻辑的弱相等性理论ＣＬｗ加入（ξ０）之后，弱相等性被加强为ξ０相等性．作者证明ξ０相等性严格强于弱相等性，但严格弱于组合β相等性，作者给出ξ０相等性的有穷公理化．     

群众决策的ak—较多规则

对于群体决策问题，本文给出一个新的带参数的ａｋ－较多规则，并且讨论了在此规则下个体选优解和群体选优解的关系，此外，还论证了相应的ａｋ－较多规则满足Ａｒｒｏｗ公理的情况。     

货币政策规则的微观基础研究

本文从企业生产视角建立一个静态一般均衡模型,揭示货币政策规则更加具体的微观含义.     

Expert Rule Versus Majority Rule Under Partial Information, II

The main purpose of this paper is clarifying the connection between some characteristics of a deciding body and the probability of its making correct decisions. In our model a group of decision makers is required to select one of two alternatives. We assume the probabilities of the decision makers being correct are independent random variables distributed according to the same given distribution rule. This distribution belongs to a general family, containing the uniform distribution as a particular case. We investigate the behavior of the probability of the expert rule being optimal, as well as that of the majority rule, both as functions of the distribution parameter and the group size. The main result is that for any value of the distribution parameter the expert rule is far more likely to be optimal than the majority rule, especially as the deciding body becomes larger.     

Markov's Rule revisited

I am grateful to Boris Kushner for informing me about [Nov 43], the impetus for this note, and to Anne Troelstra for comments on an early sketch. Research partially supported by ONR grant N00014-84-K-0415 and by DARPA grant F33615-81-K-1539     

辛甫生公式的推广

给出了具有3次代数精度的条件,对辛甫生求积公式进行了推广,利用待定系数方法推导出了一般性的公式,并从该推广的方法导出了三点高斯公式.     

A generalization of Simpson's Rule

Let and let , where P _c ⁿ denoles the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively, and are each exact for all polynomials of degree ≤n+1. We let L(f)=αTM(f)+(1−α)TA(f), where , to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem 1). The case n=0 is just the classical Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P _(a+b) ^2/n+1 (x) by the Hermite cubic interpolant at a and b, we obtain some known formulae by a different approach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial of f at a and b, respectively. Of course all of our formulae can be compounded over subintervals of [a,b].     

Rule Induction in Investment Appraisal

Rule induction is a machine learning technique which has been used in knowledge acquisition for expert systems. This paper explores its use for the interpretation of the results from simulation of investment models in order to identify the major risks.     

Higher Order Fractional Leibniz Rule

The fractional Leibniz rule is generalized by the Coifman–Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.     

模糊推理中的规则约简

为避免模糊推理中出现复合规则爆炸的情况,研究了方程pΛq→r=(p→r)V(q→r)关于uninorm诱导蕴涵所有解的情况.选用uninorm诱导的R-蕴涵作为上述方程中蕴涵时,证明了没有新的非平凡解出现;选用uninorm诱导的S-蕴涵作为上述方程中蕴涵时,获得了uninorm满足该方程的充要条件.     

Simpson校正公式

给出了Simpson校正公式的截断误差,分析了复化Simpson校正公式的收敛阶.数值算例验证了理论分析的正确性.