L—fuzzy几乎良紧性的若干性质

进一步研究Ｌ－ｆｕｚｚｙ几乎良紧性的特征及其与良紧性，近似良紧性，几乎Ｆ紧性，可数良紧性和ＮＳ闭性等概念之间的关系。证明了Ｌ－ｆｕｚｚｙ几乎良紧性的是Ｌ－ｆｕｚｚｙ θ－闭遗传的拓扑不变的等重要性质。     

L-拓扑空间中的几乎超紧L-子集

在L-拓扑空间中定义了L-子集的几乎超紧性,讨论了几乎超紧L-子集的性质以及L-子集的几乎超紧性与超紧性、近似超紧性及几乎良紧性之间的关系,给出了几乎超紧L-子集的网式及滤子刻画并证明了L-拓扑空间的几乎超紧性是几乎紧性的“L-推广”.     

L—Fuzzy拓扑空间中的可数F紧性与几乎可数F紧性

本文在Ｌ－ｕｚｚｙ拓扑空间中引入可数Ｆ紧性与几乎可数Ｆ紧性的概念，并讨论了它们的性质及其相互关系。     

L-fuzzy拓扑空间中的几乎可数仿紧性

以可数仿紧性为背景,介绍几乎可数仿紧性的定义,并刻画其基本特征.深入研究L-fuzzy几乎可数仿紧性的性质,并证明几乎可敷仿紧性是"L-好的推广".     

L—fuzzy拓扑空间中的近似良紧性

本文系统地研究了Ｌ－ｆｕｚｚｙ拓扑空间中近奶紧性的特征及其拓扑性质。讨论了近似良紧性与良紧性之间的关系。证明了近似良紧性是正则闭遗传的，有限可和的以及在满层的Ｌ－ｆｕｚｚｙ拓扑空间中，对于近似良紧性而言，ＴΝＸＯＨＯＢ乘积定理成立等重要性质。     

相关远域与不分明子集的超紧性

本文引入了α－相关远域族的概念，由此写义了一般不分明子集的超紧性。这种超紧性在人间的情形与「１」中的超紧性等价，在子集的情形以良肾性为特款，具有相应的关于良紧性的几乎所有性质。特别是基于这种超仿紧性的超紧性还是Ｌ－好的推广。     

几乎仿紧空间

主要证明了如下结果 :( 1 )如果 X =∏α∈ΛXα是 |Λ | -仿紧空间 ,则 X是几乎仿紧 (仿 - L indelof)空间当且仅当 F∈ [Λ ]<ω,∏α∈ FXα是几乎仿紧 (仿 - L indelof)空间 .( 2 )如果 X =∏i∈ωXi 是可数仿紧的 ,则下列三条等价 :X是几乎仿紧 (仿 - L indelof)的 : F∈ [ω]<ω,∏i∈ FXi是几乎仿紧 (仿 - L indelof)的 : n∈ω,∏i≤ nXi是几乎仿紧 (仿- Lindelof)的 .最后还给出了几乎仿紧 (仿 - L indelof)空间的一个刻划     

3族新的不含紧优与几乎紧优的有向双环网络无限族

给出了3族新的不含紧优与几乎紧优的有向双环网络.     

L－fuzzy拓扑空间中的近似良紧性

本文系统地研究了Ｌ－ｆｕｚｚｙ拓扑空间中近似良紧性的特征及其拓补性质。讨论了近似良紧性与良紧性之间的关系。证明了近似良紧性是正则闭遗传的，有限可和的以及在满层的Ｌ—ｆｕｚｚｙ拓扑空间中，对于近似良紧性而言，ＸＯＨＯＢ乘积定理成立等重要性质。     

最优双环网络的无限族

本文提出了找到紧优和几乎紧优DLN的无限族的一种方法,并据此给出了一系列新的无限族。最后列表显式展示了69个紧优和33个几乎紧优DLN的无限族,使得对每个N,4≤N≤300,这102个无限族中有N个结点的DLN。     

Regularly open sets in fuzzy topological spaces

This paper is devoted to the study of the role of fuzzy regularly open sets. We prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings. We prove that under a fuzzy almost continuous and fuzzy almost open map, the inverse image of a fuzzy regularly open set is fuzzy regularly open. Further we define a new type of fuzzy separation axioms, fuzzy almost separation axioms. It is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology. For example, in a fuzzy almost T₁ space not every fuzzy singleton is δ-closed. Also a fuzzy space which is fuzzy almost as well as fuzzy almost T₀ is fuzzy almost regular. While in general topology we have to take an almost T₂ space in place of almost T₀ space.     

Almost compactness in fuzzy topological spaces

We introduce and study almost compactness for fuzzy topological spaces. We show that the almost continuous image of an almost compact fuzzy topological space is almost compact. Moreover, we show that generally almost compactness for fuzzy topological spaces is not product-invariant, but if X and Y are almost fuzzy topological spaces and X is product related to Y, then their fuzzy topological product is almost compact.     

Almost periodic fuzzy-number-valued functions

In this paper we develop a theory of almost periodic fuzzy functions, i.e. of the almost periodic functions of real variable and with values fuzzy real numbers, Although the class of fuzzy real numbers does not form a linear normed space, the majority of main properties of almost periodic functions with values in Banach spaces are extended to this case. Applications to fuzzy differential equations and to (fuzzy) dynamical systems are given.     

On fuzzy almost continuous convergence in fuzzy function spaces

In this paper, we study the fuzzy almost continuous convergence of fuzzy nets on the set FAC(X, Y) of all fuzzy almost continuous functions of a fuzzy topological space X into another Y. Also, we introduce the notions of fuzzy splitting and fuzzy jointly continuous topologies on the set FAC(X, Y) and study some of its basic properties.     

模糊化的Egoroff定理

在一般模糊测度空间上,针对可测模糊值函数序列给出了几乎处处收敛,几乎一致收敛和伪几乎一致收敛的概念,并在此基础上,进一步研究了这几种收敛的蕴涵关系,从而获得了模糊化的Egoroff定理,使模糊值函数序列的理论得到进一步丰富.     

(O,N)-蕴涵的新性质

重叠函数是一类特殊的非结合的二元聚类函数.利用重叠函数可以诱导出不同形式的模糊蕴涵.文[7]介绍了由重叠函数O和模糊否定N诱导出的模糊蕴涵—(O,N)-蕴涵,并对(O,N)-蕴涵的基本性质进行了研究,但尚存一些重要性质尚未得到研究.主要基于自同构φ和模糊否定N的相关性质对(O,N)-蕴涵进行深入研究,给出(O,N)-蕴涵一些新的重要性质.     

Fuzzy uniqueness of fuzzy mappings

For fuzzy mappings between fuzzy sets of higher level we study a notion of fuzzy uniqueness. i.e. of fuzzy functions, which formalizes the intuition that ‘almost identical’ images under f.Characterizations are given for such fuzzy mappings which are really (i.e. with truth value 1) fuzzy unique or fuzzy biunique, and for those fuzzy sets which can be domains of really fuzzy unique fuzzy mappings.Finally, as an application fuzzy cardinals, their ordering, sum, and product are introduced, and some properties proved.     

Asymptotic structural characteristics of fuzzy measure and their applications

In fuzzy measure theory, as Sugeno's fuzzy measures lose additivity in general, the concept ‘almost’, which is well known in classical measure theory, splits into two different concepts, ‘almost’ and ‘pseudo-almost’. In order to replace the additivity, it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called ‘waxing’ and ‘waning’, and to introduce some new concepts, such as ‘autocontinuity’, ‘converse-autocontinuity’ and ‘pseudo-autocontinuity’. These concepts describe some asymptotic structural characteristics of a fuzzy measure.In this paper, by means of the asymptotic structural characteristics of fuzzy measure, we also give four forms of generalization for both Egoroff's theorem, Riesz's theorem and Lebesgue's theorem respectively, and prove the almost everywhere (pseudo-almost everywhere) convergence theorem, the convergence in measure (pseudo-in measure) theorem of the sequence of fuzzy integrals. In the last two theorems, the employed conditions are not only sufficient, but also necessary.     

Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a sequence of fuzzy numbers is strongly almost lacunary convergent with respect to an Orlicz function then it is almost lacunary statistical convergent.     

COMPLETENESS IN LINEAR FUZZY NEIGHBORHOOD SPACES

Abstract

Some of the problems related to the completeness in linear fuzzy neighborhood spaces are investigated. It is shown that if (E, N) is a linear fuzzy neighborhood space, then the space É = M(E) of all minimal hyper-Cauchy prefilters on (E, N), equipped with a certain linear fuzzy neighborhood structure N, is the unique, up to isomorphism, ultracompletion of (E, N).