一种基于语言变量的多属性决策ELECTRE方法

基于语言变量的多属性决策问题,提出了一种ElECTRE决策方法.首先将决策属性的语言评价值转变成三角模糊数,通过三角模糊数可能度的计算公式,将指标值从三角模糊数映射到优劣关系等价的实数值,然后利用改进的ELECTREII方法计算各方案之间的相对优势度矩阵和相对劣势矩阵,进一步求出方案之间的修正综合加权矩阵和各方案净优势值,根据各方案净优势值大小确定方案的优劣排序,最后通过应用实例表明,该方法简单明了,易于推广使用.     

模糊数排序的可能度方法

由两个模糊数的隶属函数确定三个面积,据此建立一个对模糊数进行大小比较的可能度计算公式.公式表达式非常简洁,同时还具有传递性、互补性等诸多良好的性质,因而具有很强的实用性和可操作性.对给定的一组模糊数,先利用两两比较的结果建立一个可能度矩阵,同时给出基于可能度矩阵的模糊数排序算法.最后给出一个排序算法的实例.     

梯形模糊有序加权几何算子及其在决策中的应用

针对梯形模糊数据信息的集成问题,给出了梯形模糊数两两比较的可能度公式和梯形模糊有序加权几何(TFOWG)算子.基于可能度公式和TFOWG算子,提出了一种准则权重信息完全未知且准则值以梯形模糊数形式给出的不确定多准则决策方法.最后,实例分析表明了该方法的可行性和有效性.     

直觉模糊数的序优先度及其在群评价中的应用

直觉模糊数是处理模糊问题的一种有效的信息表达形式,其排序方法是研究的热点问题之一.基于均匀分布的原理,提出新的直觉模糊数序优先度的概念,给出各种情形下的序优先度的计算公式,并探讨了直觉模糊数序优先度的若干性质.给出了基于直觉模糊数序优先度的群评价算法.实例分析表明本文提出的方法是可行有效的.     

不确定多属性决策中的一种模糊赋权方法

研究了以三角模糊数给出属性权重的不确定多属性决策问题,提出了一种基于三角模糊数的赋权方法,并给出了决策模型.首先决策者将属性权重两两比较的结果用三角模糊数表示,构造三角模糊数互补判断矩阵.通过求解矩阵得到模糊权重.然后,集结各方案的模糊综合属性值,通过构造并求解可能度矩阵对方案进行排序.最后给出了一个应用实例.     

基于包含度的模糊随机粗糙集模型

针对随机性与模糊性同时存在的情形,提出了建立在模糊随机近似空间上的基于包含度的模糊随机粗糙集模型.首先给出了模糊随机近似空间的概念,然后利用包含度提出了模糊随机近似空间上的一种基于模糊随机集的粗糙近似算子.最后讨论了这种近似算子的一些性质.     

区间直觉模糊数的序优先度及其在群评价中的应用

区间直觉模糊数是处理模糊问题的一种准确且细腻的信息表达形式,其排序方法也是当今研究的热点问题之一.基于范数理论,提出一种新的概念:区间直觉模糊数的序优先度,给出相应的序优先度的计算公式,并探讨了区间直觉模糊数的序优先度的一些性质,同时给出基于区间直觉模糊数的序优先度的群评价算法,最后结合实例表明本文提出的方法是有效、可行的.     

一种基于散度的模糊数排序方法

引用一种距离测度及模糊数的权重面积,建立了一种基于散度的模糊数排序指标.新的排序指标不仅引入了两个参考对象,即两个模糊数的极大和极小(M),(N),同时还考虑了模糊数本身的影响和决策者的决策态度.排序方法不仅计算简单、易于操作,而且还具有良好的性质.算例分析表明本文所提出的排序方法在一定程度上克服了现有方法的缺陷.     

基于可能度的三角模糊数互补判断矩阵排序方法

研究了决策信息为三角模糊数形式给出的互补判断矩阵排序问题.根据三角模糊数互相比较的可能度公式,提出一种基于可能度的三角模糊数互补判断矩阵的排序方法.该方法思路清晰、合理,计算简洁,易于上机实现.最后算例分析表明,该方法是可行、有效的.     

3PLS物流设施网络评价的模糊数据包络方法

3PLS物流设施布局直接关系到企业的战略和运作两个层面,对若干初始方案进行评价是保证物流设施布局方案有效性的前提.针对物流设施布局方案评价问题的同质性和模糊性特征,利用三角模糊数表示评价过程中的模糊不确定因素,并提出基于模糊数据包络方法的方案评价框架.通过对算例的评价应用,说明了方法的合理性和有效性.     

K故障下确定最优可测试成分的新方法

本提出了在模拟线性电路故障诊断中K故障假设下一组最优可测试成份确定的方法,它是基于电路的可测试值计算规范式不确定性组的确定,所提出的步骤与故障定位方法无关。     

Heisenberg's Inequality and Logarithmic Heisenberg's Inequality for Ambiguity Function

In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1}!.     

交叉熵——计算语言学消歧的一种工具

歧义问题的描述和消除问题是制约计算语言学发展的瓶颈问题.将交叉熵引入计算语言学消岐领域.采用语句的真实语义作为交叉熵的训练集的先验信息,将机器翻译的语义作为测试集后验信息,计算两者的交叉熵,并以交叉熵指导对歧义的辨识和消除.实例表明,该方法简洁有效,易于计算机自适应实现,交叉熵不失为计算语言学消岐的一种较为有效的工具.     

A defense of indeterminism

My goal is to defend the indeterminist approach to vagueness, according to which a borderline vague utterance is neither true nor false. Indeterminism appears to contradict bivalence and the disquotational schema for truth. I agree that indeterminism compels us to modify each of these principles. Kit Fine has defended indeterminism by claiming that ordinary ambiguous sentences are neither true nor false when one disambiguation is true and the other is false. But even if Fine is right about sentences, his point does not seem to generalize to utterances. What the indeterminist needs -- and what ordinary ambiguity does not provide -- is an ambiguous utterance where what is being said is indeterminate between two different propositions. I will show that such cases exist. These cases imply that the modifications that indeterminism makes to bivalence and the disquotational schema are required independently of indeterminism, in fact independently of vagueness.     

Infinite class of new sign ambiguities

In 1934, two kinds of multiplicative relations, the norm and the Davenport-Hasse relations, between Gauss sums, were known. In 1964, H. Hasse conjectured that the norm and the Davenport-Hasse relations were the only multiplicative relations connecting Gauss sums over Fp. However, in 1966, K. Yamamoto provided a simple counterexample disproving the conjecture. This counterexample was a new type of multiplicative relation, called a sign ambiguity, involving a ± sign not connected to elementary properties of Gauss sums. In this paper, we give an explicit product formula involving Gauss sums which generates an infinite class of new sign ambiguities, and we resolve the ambiguous sign by using Stickelberger?s theorem.     

V@R representation theorems in ambiguous frameworks

The value at risk (V@R) is a very important risk measure with significant applications in finance (risk management, pricing, hedging, portfolio theory, etc), insurance (premium principles, optimal reinsurance, etc), production, marketing (newsvendor problem), etc. It also plays a critical role in regulation about risk (Basel, Solvency, etc), it is very appreciated by practitioners due to its intuitive interpretation, and it is the unique popular risk measure remaining finite for heavy tailed risks with unbounded expectation. Besides, ambiguous frameworks are becoming more and more usual in applications of risk analysis. Lack of data or committed errors may provoke discrepancies between real probabilities and estimated ones. This paper combines both V@R and ambiguous settings, and a new representation theorem for V@R is given. Consequently, inspired by previous studies dealing with coherent risk measures and their representation, we will give new methods to compute and optimize V@R under ambiguity. This seems to be a relevant finding because the analytical properties of V@R are very weak if one compares with a coherent risk measure. Indeed, V@R is neither continuous nor convex, which makes it very complicated to deal with it in mathematical approaches. Nevertheless, the results of this paper will allow us to transform computation and optimization problems involving V@R into continuous and differentiable problems.     

Identification and definition of lexically ambiguous words in statistics by tutors and students

Lexical ambiguity arises when a word from everyday English is used differently in a particular discipline, such as statistics. This paper reports on a project that begins by identifying tutors’ perceptions of words that are potentially lexically ambiguous to students, in two different ways. Students’ definitions of nine lexically ambiguous words are also collected at the beginning and end of a semester of introductory statistics study, in a complex design taking account of multiple tutors and multiple words in multiple contexts. Tutor perceptions and actual student difficulties at the beginning of a semester are compared. The lexical ambiguity associated with the word ‘significance’ is shown to be evident in students even after completing an introductory statistics course.     

Large deviation principle for diffusion processes under a sublinear expectation

We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential equation.As an application,we establish a large deviation principle of the Freidlin and Wentzell type under the corresponding nonlinear probability for diffusion processes with a small diffusion coefficient.     

带有模糊信息的多目标决策问题的改进灰模糊算法

将模糊数学和灰色理论结合在一起 ,针对目前复杂大系统的多目标决策问题 ,提出了一个简单实用而且有效的灰模糊求解方法 ,通过隶属函数的一致性使确定型指标和模糊型指标能融合在同一个决策中加以考虑 ,同时又介绍了一种与隶属度相关的确定权重的灰模糊方法