模糊度定义的不一致性及其理论分析

指出模糊度定义的不一致性，并通过实例进行验证；从理论上分析模糊度定义的不一致性产生的原因，指出当模糊度理论在图像处理中应用时模糊度定义的不一致性可能会产生的影响；给出一个比较合理的模糊度定义。文中提出的问题是在工程应用过程中发现的新问题，所做的工作也只是初步的。     

依零测度的Fuzzy集运算

给出了Fuzzy集合依零测度的包含,依零测度的相等。依零测度的并．交,补运算等。并补充地研究了这些基本运算,获得了若干好的性质。Fuzzy集依零测度的基本运算比标准fuzzy集合论的相应运算更有人情味,更为接近人的智能机理。有望在智能信息处理和软计算领域取得好的应用。     

模糊复测度空间上可测函数列几种收敛性之间的关系

作为经典复测度和模糊测度的推广,研究模糊复测度及模糊复测度空间上可测函数列几种收敛性之间的关系.在模糊复测度空间上得到了Egoroff定理、Lebesgue定理和Riesz定理等重要结果.为模糊复分析的深入研究打下一定基础.     

模糊熵,距离测度和散度测度

在模糊集的运算基础上,讨论如何用模糊熵定义模糊距离测度,并且研究了模糊距离测度和散度测度的关系。     

包含度和贴近度的相互诱导关系

基于贴近度和包含度的公理化定义，给出贴近度和包含度之间的相互诱导关系，建立模糊熵、贴近度和包含度之间的联系。     

Characterizations of degree one bivariate measures of concordance

We call a measure of concordance κ of an ordered pair (X,Y) of two continuous random variables a bivariate measure of concordance. This κ may be considered to be a function κ(C) of the copula C associated with (X,Y). κ is considered to be of degree n if, given any two copulas A and B, the value of their convex sum, κ(tA+(1−t)B), is a polynomial in t of degree n. Examples of bivariate measures of concordance are Spearman’s rho, Blomqvist’s beta, Gini’s measure of association, and Kendall’s tau. The first three of these are of degree one, but Kendall’s tau is of degree two. We exhibit three characterizations of bivariate measures of concordance of degree one.     

直觉模糊集的距离测度

直觉模糊集的距离测度是两个直觉模糊集差异性大小的度量,许多学者围绕其公理化定义和具体表达公式做了大量的工作,并且被广泛应用在多属性决策、模式识别等许多方面。基于直觉模糊集距离测度的公理化定义,本文对一些学者提出的距离测度公式进行了探讨,并给出了几种一般化构造形式。     

A mathematical programming problem with singular mixed pointwise-integral constraints

We investigate an infinite dimensional optimization problem which constraints are singular integral-pointwise ones. We give some partial results of existence for a solution in some particular cases. However, the lack of compactness, even in L¹ prevents to conclude in the general case. We give an existence result for a weak solution (as a measure) that we are able to describe. The regularity of such a solution is still an open problem.     

区间值直观模糊集的相似测度和距离测度

对现有的模糊集和直观模糊集的相似测度和距离测度的公理化定义进行分析,并做出改进;然后提出区间值直观模糊集的相似测度和距离测度的公理化定义,并各引入它们的一种计算方法;最后给出区间值直观模糊集的相似测度和距离测度在模式识别中的一个应用实例.     

模糊数测度空间上模糊值函数的模糊值积分的Fubini定理

建立卡氏积空间 (X×Y,S× T)上的乘积区间值测度和乘积模糊值测度 ,证明模糊值测度空间上模糊值函数的模糊值积分的 Fubini定理。     

Choquet积分的收敛定理

Murofushi、Sugeno等学者已对关于模糊测度的Choquet积分进行了详细的研究,但关于积分的收敛理论是不够的。本文讨论这一问题,给出Choquet积分的一些收敛定理,包括广义单调收敛定理、Fatou引理等。从中可以看出,Choquet积分与Sugeno模糊积分具有相同的收敛定理。     

Applications of control theory to economic analysis: J.D. Pitchford and S.J. Turnovsky,Editors, Amsterdam: North-Holland, 1977, 364 pages,Dfl. 155.00

A.K. Sen's index, P, is the only measure of poverty in a population that adequately allows for numbers in poverty, intensity of average poverty, and income distribution among the poor, while respecting two natural axioms. Nevertheless, the derivatives of P possess at least four attributes, at best highly counter-intuitive, at worst inconsistent with diminishing-marginal-utility assumptions, underlying the axioms themselves. Due to problems in handling income distribution among the poor, no measure of aggregate poverty can be constructed. Instead, it is proposed to construct a simple measure of those in ultra-poverty - among whom income cannot be very unequal - plus a pair of measures of moderate poverty.     

On classical analogues of free entropy dimension

We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension.     

Computability of measurable sets via effective topologies

We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations of the computable topological spaces constructed. The authors are supported by grants of NSFC and DFG.     

Probability Approaches to Spatially Homogeneous Boltzmann Equations

Abstract

This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p > 2).     

Distinction between several subsets of fuzzy measures

In this paper, we place several fuzzy measure subsets in relation one with the other. The subsets under study are those corresponding to the definitions of probability measure. Sugeno's g_λ-measure, Shafer's belief function and Zadeh's possibility measure. We study the intersection of these subsets and we show the particular role of Dirac's measures in this comparison. We limit ourself to the case of mappins whose domain is the collection of all subsets of a finite set.Finally, the obtained partial results are summarized in only one figure which shoul clarify the specificity of each of the above definitions.     

Oscillation of delay differential equations on time scales

Consider the following equation: , where t is in a measure chain. We apply the theory of measure chains to investigate the oscillation and nonoscillation of the above equation on the basis of some well-known results. And in some sense, we show a method to unify the delay differential equation and delay difference equation.     

An existence result for superparabolic functions

We study superparabolic functions related to nonlinear parabolic equations. They are defined by means of a parabolic comparison principle with respect to solutions. We show that every superparabolic function satisfies the equation with a positive Radon measure on the right-hand side, and conversely, for every finite positive Radon measure there exists a superparabolic function which is solution to the corresponding equation with measure data.