具有模糊系数的模糊线性规划问题

本文考虑具有模糊系数的模糊线性规划问题中各系数的模糊可能性分布，而用指数（或线性）的隶属函数来描述，然后使用模糊数集上的实值函数，使模糊数在模型均值的意义下对应于一个实数，借此，将原问题公式化为一个普通线性规划。     

四元数矩阵方程AX=B的实部半正定解(英文)

一个ｎ×ｎ实四元数矩阵称为实部半正定（或正定）矩阵，如果对于任意的非零ｎ维四元数列向量ｘ，有Ｒｅ［ｘＡｘ］≥０（或＞０）．本文给出了四元数矩阵方程ＡＸ＝Ｂ有实部半正定（或正定）矩阵解的充要条件及其通解的表达式，并给出了四元数分块阵为实部半正定（或正定）矩阵的一个判别法则     

一种对方案有偏好的三角模糊数多属性决策方法

研究了属性权重不能完全确知,方案属性值和偏好值均为三角模糊数的多属性决策问题.通过分析相关文献中利用方案属性值与偏好值之间的偏差求出属性权重的不合理性,在最小化方案综合属性值与偏好值偏差的基础上,建立并求解一个规划模型而得到属性权重.然后,利用三角模糊数的可能度公式及互补判断矩阵的排序公式,获得决策方案的排序,从而得到对方案有偏好的一种三角模糊数多属性决策方法.最后,通过计算实例说明了该方法.     

关于Katai的一个猜想的证明

本文证明了：如果实值加性函数ｆ（ｎ）满足条件‖ｆ（ｎ＋１）－ｆ（ｎ）‖＝ｏ（１），（ｎ→∞）这里‖‖表示一实数与最近的整数的距离，则一定有某常数ｃ使ｆ（ｎ）一ｃｌｏｇｎ为整数值加性函数．这证实了ＫａｔａｉⅠ的一个猜想．     

加性函数的一个结果的简单证明

以‖ｘ‖表示ｘ与其最近的整数的距离．本文给出了如下结果的一个简化证明：如果一实值加性函数ｆ（ｎ）满足条件‖ｆ（ｎ＋１）─ｆ（ｎ）‖＝Ｏ（１）（ｎ→∞）；则存在一常数Ｃ，使得ｆ（ｎ）—Ｃｌｏｇｎ为整值加性函数．     

双等差数列

双等差数列高鸿宾（云南省呈贡县一中６５０５００）在解一个动态规划习题时得到一个数列５，１３，２０，２８，３５，４３，５０，（１）另外又有数列１；０，２，１，３；２，４，（２）如何求出它们的通项公式和前ｎ项和公式呢？在数列（１）中，从第二项开始，每一项...     

一组与有关的数学分析问题

一组与有关的数学分析问题石心坦，杨凌（合肥工业大学）（蚌埠教育学院）众所周知，“０”和“１”是两个重要的实数，然而下面的一组数学分析问题却与有密切关系。有趣的是，这些问题从表面上看似乎与无关，但问题的结果却是或与某些常数的乘积，从而说明了数所具有的...     

模糊向量空间中模糊基的判定方法及其维数的计算

本文在（１）的基础上给出了模糊基的另一种构造方法，由此得到了模糊基的判定方法。研究了基的μ值分布状况，最后给出了模糊向量空间维数的计算方法。     

模糊错误二类1矩阵方程实解的存在性及其解法

本文在文（７）的基础上研究了模糊错误二类１矩阵方程实解的存在性和它的基本求解方法。     

三角模糊数互补判断矩阵排序的目标规划法

针对决策者以三角模糊数互补判断矩阵形式给出的多目标决策问题.给出三角模糊数加性一致性互补判断矩阵的判定定理.利用该定理基于最小偏差建立一个目标规划模型而解得三角模糊数互补判断矩阵的权重向量,从而使用三角模糊数排序公式对方案排序,提出了基于目标规划的三角模糊数互补判断矩阵排序法.最后,将模型与方法应用于项目投资决策中.     

Extended and Unscented Kalman filtering based feedforward neural networks for time series prediction

With the ability to deal with high non-linearity, artificial neural networks (ANNs) and support vector machines (SVMs) have been widely studied and successfully applied to time series prediction. However, good fitting results of ANNs and SVMs to nonlinear models do not guarantee an equally good prediction performance. One main reason is that their dynamics and properties are changing with time, and another key problem is the inherent noise of the fitting data. Nonlinear filtering methods have some advantages such as handling additive noises and following the movement of a system when the underlying model is evolving through time. The present paper investigates time series prediction algorithms by using a combination of nonlinear filtering approaches and the feedforward neural network (FNN). The nonlinear filtering model is established by using the FNN’s weights to present state equation and the FNN’s output to present the observation equation, and the input vector to the FNN is composed of the predicted signal with given length, then the extended Kalman filtering (EKF) and Unscented Kalman filtering (UKF) are used to online train the FNN. Time series prediction results are presented by the predicted observation value of nonlinear filtering approaches. To evaluate the proposed methods, the developed techniques are applied to the predictions of one simulated Mackey-Glass chaotic time series and one real monthly mean water levels time series. Generally, the prediction accuracy of the UKF-based FNN is better than the EKF-based FNN when the model is highly nonlinear. However, comparing from prediction accuracy and computational effort based on the prediction model proposed in our study, we draw the conclusion that the EKF-based FNN is superior to the UKF-based FNN for the theoretical Mackey-Glass time series prediction and the real monthly mean water levels time series prediction.     

Real-time stable self-learning FNN controller using genetic algorithm

A kind of real-time stable self-learning fuzzy neural network (FNN) control system is proposed in this paper. The control system is composed of two parts: (1) A FNN controller which use genetic algorithm (GA) to search optimal fuzzy rules and membership functions for the unknown controlled plant; (2) A supervisor which can guarantee the stability of the control system during the real-time learning stage, since the GA has some random property which may cause control system unstable. The approach proposed in this paper combine a priori knowledge of designer and the learning ability of FNN to achieve optimal fuzzy control for an unknown plant in real-time. The efficiency of the approach is verified by computer simulation.     

基于集对分析的混合型多属性决策方法的研究

针对属性权重信息不完全且属性值为实数、区间数和模糊语言值相结合的混合型多属性决策问题,提出了一种基于集对分析的多属性决策方法.该方法所需计算量较少,方法简单,易于计算.最后通过实例验证了该方法的有效性和实用性.     

三层前向神经网络的一致逼近性

近年来，前向神经网络泛逼近的一致性分析一直为众多学者所重视。本文系统分析三层前向网络对于拟差值保序函数族的一致逼近性，其中，转换函数σ是广义Sigmoidal函数。并将此一致性结果用于建立一类新的模糊神经网络(FNN)，即折线FNN．研究这类网络对于两个给定的模糊函数的逼近性，相关结论在分析折线FNN的泛逼近性时起关键作用。     

模糊离散事件动态系统及模糊数输入法仿真技术

本文以时间论域上的模糊集为基本模糊事件，定义了模糊离散事件动态系统，给出了系统的数学模型，以ＦＭ／ＦＭ／１排队系统为例，演示了模糊数输入法仿真技术，给出了有关结果，为管理系统仿真应用模糊集理论提出了一条新的途径。     

Fuzzy hierarchical analysis

This paper extends hierarchical analysis to the case where the participants are allowed to employ fuzzy ratios in place of exact ratios. If a person considers alternative A more important than alternative B, then the ratio used might be approximately 3 to 1, or between 2 to 1, and 4 to 1, or at most 5 to 1. The pairwise comparison of the issues and the criteria in the hierarchy produce fuzzy positive reciprocal matrices. The geometric mean method is employed to calculate the fuzzy weights for each fuzzy matrix, and these are combined in the usual manner to determine the final fuzzy weights for the alternatives. The final fuzzy weights are used to rank the alternatives from highest to lowest. The highest ranking contains all the undominated issues. The procedure easily extends to the situation where many experts are utilized in the ranking process, or to the case of missing data. Two examples are presented showing the final fuzzy weights and the final ranking.     

Minimization approach to membership evaluation in fuzzy sets and error analysis

Evaluation of the degree of membership in fuzzy sets is a fundamental topic in fuzzy set theory. Saaty (Ref. 1) proposes a method for solving this problem that has been widely accepted. In this paper, we examine the problem from an error minimization point of view that attempts to reflect the real intentions of the decision maker. When this approach is used, the findings reveal that fuzzy sets of different cardinalities have dramatically different requirements in the consistency level of the input data as far as the error minimization criterion is concerned.     

一类模糊不动点定理及其应用

在半序模糊距离空间中,讨论了一类单调模糊映射的性质,并且把其应用于研究RegularFNN和解模糊方程.     

O型模糊数及其结构元表示方法

为研究平面或空间模糊几何问题的需要,在平面或空间模糊点的背景下,给出了O型模糊数的概念,它是一类二维实数域上的模糊集,同时给出了O型模糊数的二维模糊结构元表示方法.二维模糊数的结构元方法,可以使O型模糊数的运算变成普通实数与模糊结构元之间的运算,使得过去必须依赖扩张原理和表现定理来刻画的模糊数运算变得更加简单与直观,不仅仅为模糊分析计算的简化提供了工具,也为二维实数域上模糊分析理论与应用的研究开创了一条新的途径.