广义可加Fuzzy测度

本文首先引入Fuzzy集类上（广义）可加Fuzzy测度的有关概念，然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理，最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。     

三个测度猜想的否定

给出三个非常容易让人误以为真的测度猜想,通过定理与λ-Cantor集及其余集的构造给出三个猜想的否定答案.     

切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用,证明了Marstrand定理.     

切测度的几何分析

本文研究了Radon测度μ的切测度,给出了切测度的Rectifiability.利用对偶性原理及Blow-up 技巧证明了连续函数的微切集的存在性.另外,本文给出了切测度的平坦性特征.作为切测度的应用, 证明了Marstrand定理.     

基于分解测度的模糊积分及收敛定理Mamadou Traore

为了解决一些收敛定理,我们给出基于半环([0,1],, )的伪可加分解测度的积分这种模糊积分被深入研究.在给出这种积分的性质的基础上,我们得到一些收敛定理,它们是经典收敛定理的扩张,同时我们得到关于这种模糊测度的Egorof定理.     

基于分解测度的模糊积分及收敛定理(英文)

为了解决一些收敛定理 ,我们给出基于半环 ( [0 ,1 ], , )的伪可加分解测度的积分这种模糊积分被深入研究 .在给出这种积分的性质的基础上 ,我们得到一些收敛定理 ,它们是经典收敛定理的扩张 ,同时我们得到关于这种模糊测度的 Egorof定理     

类切饼集的测度维数

本文考虑了满足一定条件的类切饼集,主要利用密度定理,获得其Hausdorff测度和填充测度是等价的.同时,给出这类类切饼集维数和测度的统计解释.     

F集上的可能性测度与一致信任函数扩张全体的半格结构

本文提出了Fuzzy集合上的可能性测度与一致信任函数两个概念,并得到可能性测度扩张与一致信任函数扩张两个重要定理,同时,还讨论了扩张全体的代数结构。     

连续测度扩张

本文给出了交封闭集类上定义的一般连续测度（可取值＋∞）可被扩张到包含这个集类的最小单调类上的充要条件和存在唯一扩张的条件，证明了在单调类上进一步扩张的存在性。     

集值测度的延拓定理

讨论了集值测度的若干基本性质，在此基础上，研究了集值测度凸性，紧性及其靠拢定理，特别是到紧凸值集值测度的延拓定理。     

On the Extension of D-Poset Valued Measures

A variant of Alexandrov theorem is proved stating that a compact, subadditive D-poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.     

Convex extensions of the convex set valued maps

In this article the existence of the convex extension of convex set valued map is considered. Conditions are obtained, based on the notion of the derivative of set valued maps, which guarantee the existence of convex extension. The conditions are given, when the convex set valued map has no convex extension. The convex set valued map is specified, which is the maximal convex extension of the given convex set valued map and includes all other convex extensions. The connection between Lipschitz continuity and existence of convex extension of the given convex set valued map is studied.     

半非紧测度与集值AM映象

本文以半非紧测度为工具研究一类非线性集值映象的性质，然后把所得结果用于证明微分包含的解的存在性     

On the theory of Banach space valued multifunctions. 2. Set valued martingales and set valued measures

This second part of the work on Banach space valued multifunctions begins with a detailed study of set valued martingales, which have their values in a Banach space. Several new convergence theorems are established for different modes of convergence. The profile of a multifunction in connection with set valued martingales is also studied. The notion of weak convergence of multifunctions is introduced and used to obtain additional convergence theorems for set valued martingales. In the last two sections of the paper set valued measures dealt with and an integral with respect to a set valued measure is introduced.     

Banach空间中集值测度的表示定理

本文在可分自反Ｒａｎａｃｈ空的的情形下，给出了任何一列两两等比、一致有界的矢值测度可以生成一个有界闭凸值集值测度的所谓表示定理，而这个定现对κ空间首先在［３］中建立。同时，找到了由一列两两等比、一致有界变差矢值测度所生成集值测度与这列矢值测度Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ导数之间的关系。     

Single valued neutrosophic cross-entropy for multicriteria decision making problems

A single valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which give us an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exist in real world. It would be more suitable to apply indeterminate information and inconsistent information measures. In this paper, the cross entropy of SVNSs, called single valued neutrosophic cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multicriteria decision-making method based on the proposed single valued neutrosophic cross entropy is established in which criteria values for alternatives are SVNSs. In decision making process, we utilize the single-valued neutrosophic weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example of the choosing problem of suppliers is provided to illustrate the application of the developed approach.     

马尔可夫过程H-值可加泛函的向前向后鞅分解

本文研究了马尔可夫H-值可加泛函的向前向后鞅分解.利用Lyons-Meyer-Zheng鞅分解得到了泛函数极限定理所必需的极大不等式和紧性结果,在最小条件限度内得到了马尔可夫过程经验测度的泛函中心极限定理,将该定理从实值情形推广到了希尔伯特值情形.     

渐近纠缠算子单值扩张性质的等价性

算子T∈B(H)称作有单值扩张性质,若对任意一个开集U■C,满足方程(T-λI)f(λ)=0(λ∈U)的唯一的解析函数为零函数.显然,当int σ_p(T)=时,T有单值扩张性质,其中σ_p(T)为T的点谱.本文给出了渐近纠缠算子单值扩张性质的稳定性的等价条件,同时研究了2×2上三角算子矩阵的单值扩张性质的稳定性.     

Dieudonné's theorem for non-additive set functions

A Cafiero type criterion and an extension of the classical Dieudonné's theorem for a class of non-additive set functions valued into a complete Hausdorff uniform space are established.     

On the extension of measures with values in partially ordered semigroups

Clearly the sum as well as the maximum of two real numbers can be presented as a semigroup operation. So the measure with values in a partially ordered semigroup is a common generalization of additive or subadditive and maxitive measures (see Section 4). The extension of such measures we realize by the transfinite induction (see also [2]) and we use a result of [1] for real valued functions.