$I$-模糊拓扑空间中的模糊紧度

本文借助不等式给出了$I$-模糊拓扑空间中模糊紧度的概念, 并研究了相关的性质.     

模糊蕴涵与Smooth紧

1985年,Sostak[8]由逻辑的观点出发定义了一种基于Lukasiew icz蕴涵算子的Sm ooth紧,基于同样的思想A.H aydar E s[12]又定义了另外几种Sm ooth(fuzzy)紧并讨论了它们之间的关系。王国俊教授[10]提出了一种比Lukasiew icz算子具有更好性质的R0-算子,基于R0-算子我们定义了一种模糊蕴涵,通过这种模糊蕴涵定义几种Sm ooth紧并讨论了它们的一些性质。     

L-模糊SP-紧集

本文在L-模糊拓扑空间引入了一种新的紧性—SP-紧性，给出了SP-紧性的α-网，α-滤子，r-SP-覆盖，r^ -有限交性质等多种刻画．这种紧性是针对任意L-模糊子集来定义的，且保持了一般拓扑空间中紧性的许多好的性质．     

闭模糊拟阵的特征

给出Goetchel和Voxman定义的模糊拟阵成为闭模糊拟阵的三个充分必要条件。     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

模糊星形数空间在L_p度量下的紧集刻画

1990年,P.Diamond首次给出了由全体相对于原点的模糊星形数构成的空间在Lp度量下的紧集刻画。后来,Congxin Wu和Zhitao Zhao通过一个反例指出了P.Diamond的刻画是不正确的,并给出了一种正确的刻画。在这篇文章中,我们将进一步推广这个结论,得到了全体模糊星形数空间在Lp度量下的紧集刻画。     

关于模糊数空间的Skorokhod拓扑的注记

首先考察模糊数空间中Skorokhod度量与紧承下方图度量之间的关系,然后说明了文献[4]中的关于Skorokhod拓扑紧致性的例子是错误的并给出了正确的例子.     

模糊数关于紧承下方图度量的线性性质

证明了紧承下方图度量不是平移不变的.对紧承下方图度量的代数运算的连续性进行了讨论.证明了关于紧承下方图度量,模糊数空间只能是嵌入到拓扑向量空间当中,但不嵌入赋范线性空间当中.并与关于上确界度量的结果进行了比较.最后,给出了一个紧承下方图度量的下界.     

模糊赋范线性空间的紧性与完备性

讨论了Fuzzy赋范线性中准紧集、完备集及有界集间的关系;给出完备Fuzzy赋范空间的闭球套定理与Baire定理;刻画了了有限维Fuzzy赋范空间的特征。     

下方图度量下的非紧模糊数空间

证明了非紧模糊数空间E^～在下方图度量下关于模糊数的序是可逼近的。本文给出的证明方法是构造性的，从而说明了模糊数值积分如M-积分和G-积分等是可计算的。最后给出了E^～中关于下方图度量的一些分析性质。     

A theorem on sequentiality and compactness, with its fuzzy extension

An amended proof of a theorem of Franklin's on sequentiality and sequential compactness is presented, and a corresponding fuzzy version formulated using the theory of quasi-coincidence.     

不分明拓扑中的一种覆盖式紧性

本文利用包含度来区分覆盖的层次，提出了一种新的覆盖式不分明紧性并建立了其Ｔｙｃｈｎｏｆｆ定理．     

Almost Fuzzy Compactness in L-fuzzy Top ological Spaces

In this paper, the notion of almost fuzzy compactness is defined in L-fuzzy topological spaces by means of inequality, where L is a completely distributive DeMorgan algebra. Its properties are discusse...     

Local Compactness in Fuzzy Convergence Spaces

Two notions of local precompactness in the realm of fuzzy convergence spaces are investigated. It is shown that the property of local precompactness possesses a “good extension.” Moreover, for each given fuzzy convergence space, there exists a coarsest locally precompact space which is finer than the original space. Continuity between fuzzy spaces is preserved between the associated locally precompact spaces. Invariance of regularity with respect to taking locally precompact modifications is discussed.     

$L$-Fuzzy拓扑空间中的可数紧性度和Lindel\"{o}f性质度

In this paper,the concept of countable compactness degree and the concept of Lindelf property degree are defined in L-fuzzy topological spaces by means of implication operator →.Many properties of them are discussed.     

Convex fuzzy sets

This paper gathers some elementary known results about convex fuzzy sets and completes the theory, introducing the necessary concepts. Using a representation theorem for fuzzy subspaces it gives separation theorems for convex fuzzy sets in the proper setting.     

Compact G-Fuzzy topological spaces

Considering complete Boolean algebras $\text{G}$ as sets of truth values a new concept of compactness—so-called probabilistic compactness — is introduced to $\text{G}$-fuzzy topological spaces. The aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true; e.g. probabilistic compactness is preserved under projective limits, every probabilistic compact space has an unique $\text{G}$-fuzzy uniformity being compatible with the underlying $\text{G}$-fuzzy topology, etc. Finally using the selection theorem due to Kuratowski and Ryll-Nardzewski a non-trivial example of a probabilistic compact space is given.     

向量优化中有效点的存在性

分别在有pre-order的无线性结构的集合和拓扑空间中，给出了有效点的存在性。作为应用，讨论了向量优化问题中解的存在性。最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系。     

I-模糊拓扑空间中的紧度

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.